The scoring was opened 12 minutes in when a cross from Heung-min Son was bundled into his own net by Sergi Canos, and the provider turned into the scorer in the second-half when Son summoned up the finishing touch to a sweeping counter-attack which sealed Spurs the three points.
The result sees Tottenham rise to 6th in the Premier League table whilst Brentford drop down to 12th on goal difference.
Story of the game
Conte made two changes to the side that edged past Leeds United in their most recent Premier League fixture after their meeting with Burnley at the weekend was postponed due to heavy snowfall. Davinson Sanchez came in for Japhet Tanganga in defence while Oliver Skipp replaced Harry Winks in the centre of the park.
Meanwhile, Brentford were unsurprisingly unchanged after their 1-0 victory over Everton on Sunday, confirming that it would be 3-4-3 against 3-5-2 tonight — but which traditional unorthodoxy of English football would come out on top here?
The first chance of the match fell to the hosts when Harry Kane dropped into midfield and received the ball from Sergio Reguilon. The England striker then strode forward before sliding Lucas Moura through on goal, the Brazilian drawing a fine save from Alvaro Fernandez at his near post.
And it would be Tottenham who took the lead courtesy of an own goal. It came when Son played a short corner to Reguilon and received the ball straight back from the Spaniard. Son then shifted the ball onto his left-foot and delivered an in-swinging cross which was aiming for Ben Davies but was bundled into his own net by Canos.
Enjoying themselves from set-pieces, Spurs came close to doubling their advantage when a lofted Son free-kick nearly met the head of Eric Dier in the box, but the ball ultimately fell into the grateful palms of Fernandez.
Brentford's best chance of the opening half-an-hour came when the ball dropped for Bryan Mbeumo to volley 30 yards from goal. The Frenchman did brilliantly well on the volley, but the ball fizzed high and wide of the top right corner.
The Bees weren't creating enough in the final third and head coach Thomas Frank was in constant dialogue with assistant Brian Riemer about how to solve that. They were matching Tottenham everywhere except for the box they were attacking and, down to an early goal, that had to change.
Tottenham, on the other hand, were having some attacking joy, particularly through the players fielded on the left side of their line-up, and namely Son. With just under 10 minutes of the half remaining, possession was regained by Pierre-Emile Hojbjerg and released to the forward immediately. Son drove towards the box and unleashed a vicious left-footed shot which Fernandez did well to tip beyond the post and out for a corner.
On the cusp of half-time, a mishap from Fernandez — otherwise excellent in the opening 45 — nearly gave a number of Spurs players the chance to prod home following a corner, but Canos redeemed his earlier mistake by sniffing the danger and promptly clearing his lines.
The hosts came flying out of the blocks for the second half and worked a gilt-edged chance to double their advantage when Skipp played Kane through on goal. The striker bore down on Fernandez but the goalkeeper was equal to the resultant shot, much to the relief of the Brentford defence who allowed the situation to develop far too easily.
Just minutes later Skipp set Kane through in behind again, but this time the 28-year old pulled the ball back across goal. It just evaded the reach of Lucas darting in from the centre but fell to Hojbjerg on the left of the box — it was a tight angle, but the Dane was nonetheless disappointed to see his effort nestle in the net on the wrong side of the post.
Struggling to create from open play, Brentford's best chance of scoring looked likely to come from long throws delivered by Charlie Goode. Just before the hour mark, the defender supplied another arcing throw into the box and Spurs failed to clear their lines. It fell to defensive counterpart Pontus Jansson, but the skipper blazed his shot high of the crossbar.
The game turned up a notch on the 60th minute, as a handful of strong challenges boiled the blood between the teams. It initially worked in Brentford's favour as they found acres of space down the left. A neat one-two between Ivan Toney and Vitaly Janelt released the former into the box, and the midfielder cut the ball back for Toney to strike, but the resultant effort was tame.
That chance passed up felt all the more critical just moments later.
Kane picked up possession in midfield and supplied a perfectly weighted through-ball to Reguilon. The wing-back took one touch into the box before passing across goal for Son who would never miss from inside the six-yard box.
It was a beautifully crafted goal, and exactly what Spurs needed just as the Bees started buzzing.
But buzzing they still were. Frank threw Yoane Wissa and Mathias Jensen onto the pitch in a bid to push for a point, and the latter nearly pulled a goal back for Brentford when his cross-cum-shot was tipped over the bar by the back-tracking Hugo Lloris. The visitors weren't planning on giving up, but they certainly had a mountain to climb.
They had another chance to halve the deficit when a brilliant ball from Christian Norgaard reached Toney in the box. The striker so nearly squeezed it in from the tightest of angles but Lloris did remarkably well both to save and hold on to it with Brentford's forwards bearing down on him.
Brentford's final chance of the match came when Toney played the ball to Mbeumo, who twinkle-toed his way past the challenge from Ben Davies and aimed for the far top corner, but his effort was well high and wide of the target.
The visitors desperately lacked a cutting edge this evening, but take nothing away from what was an assured performance from Spurs and a deserved victory, one which makes it seven points gained from a possible nine under Conte's stewardship.
Takeaways from the match
Tottenham's left side works wonders
Son provided the troublesome cross for the opener and finalised the result by tapping home the second. The South Korean International was the best player on the pitch today, and his partnership with Reguilon down the left caused Brentford endless problems.
Conte had clearly targeted Brentford's right — comprising winger Canos at wing-back and Goode, vastly inexperienced at this level, on the right of the back three — as an area of weakness and, sure enough, Son and Reguilon proved too much for them to handle.
They were fed time and again either by Kane dropping deep or by Skipp, who was perhaps a surprise inclusion in the starting line-up tonight, but the midfielder repaid the faith Conte showed in him and then some with a faultless performance.
More creative presence needed for Brentford
Paradoxically, it seems Brentford are a better team than they give themselves credit for.
They often line-up in a 3-5-2 formation with three centre-backs, two wing-backs, and three defensive-minded midfielders. It's no wonder such a high proportion of their goals this season have come from set-pieces (six from a total of 17).
All this means that if Toney and Mbeumo aren't at their brilliant best, goals from open play will always be hard to come by. The absence of Josh Dasilva, who was instrumental in Brentford's promotion last term, is obviously being felt, but Brentford must find a workable solution in the meantime, else they'll keep losing games like this.
Tottenham Hotspur: Lloris; Sanchez, Dier, Davies; Emerson (Tanganga 83'), Hojbjerg, Skipp, Reguilon; Lucas (Winks 76'), Kane, Son (Bergwijn 87').
Unused subs: Gollini, Doherty, Sessegnon, Ndombele, Dele, Gil.
Brentford: Fernandez; Goode, Jansson, Pinnock; Canos (Wissa 70'), Onyeka (Baptiste 56'), Norgaard, Janelt (Jensen 70'), Henry; Mbeumo, Toney.
Unused subs: Cox, Roerslev, Stevens, Ghoddos, Maghoma, Forss.
Referee: Jonathan Moss
Following victory here, Tottenham play at home again on Sunday when they are visited by another newly promoted side in Norwich City.