The Gunners' Scottish left back opened the scoring, followed by a neat finish from Saka for 2-0. Lacazette scored two poacher's goals in three minutes to consolidate dominant performances from the visitors in both halves.
The result will certainly boost confidence amongst the Arsenal ranks and further drain West Brom's as they look to battle relegation this year.
Story of the match
Arsenal started the encounter strongly, looking determined to extend their good run of form under the lights of the snowy Hawthorns. Mikel Arteta's men managed to muster two shots on target within the first 10 minutes but both Saka and Hector Bellerin's efforts on goal were met with ease by the Baggies' keeper Sam Johnstone.
The visitors continued the game on top and came close again in the 15th minute when Saka's whipped cross from the right hand side just escaped the touch of Pierre-Emerick Aubameyang, who surely would have turned it home with even the slightest of touches.
It would be the home side that conjured up the best chance of the game so far as Matt Phillips chased a looping ball over the Gunners' defence, only to hit a half volley straight at stopper Bernd Leno.
By the 20 minute mark, the snowfall became heavier, and so did the pressure on West Brom's defence. The deadlock was broken two minutes later for Arsenal by an unlikely scorer in Tierney. After cleverly deceiving his opposite full back, he cut inside and bent a sweet strike into the corner on his weak foot which the goalkeeper wasn't at all expecting.
Things got even better for Arteta's men shortly after at 28 minutes when the visitors scored again after some impressive quick passing.
Young Saka started the move, finding Lacazette, who teed up Emile Smith-Rowe to square the ball back to the orchestrator of the move, who gobbled up the easy finish. It was the number seven's 3rd Premier League goal of the season.
Sam Allardyce's side could not come up with any response in the remaining minutes of the 1st half, with Lacazette and the rest of the front line dominating in the opposite box. The French striker had two efforts tipped over the bar by the keeper in the space of 10 minutes.
Martin Atkinson's half time whistle was welcomed by the home side they would have to work out how to prevent another consecutive embarrassment at the Hawthorns.
The Baggies boss' words at half time seemed to have got through to the players as Callum Robinson smashed in a rebounded effort only two minutes into the second half, but it was ruled out by a late off side flag.
15 minutes after the restart, the game continued to display the same scenes : Allardyce barking angry orders at his players whilst Arsenal's forwards kept up a flawless performance.
At the hour mark, after having a shot saved on the line, Lacazette made it 3-0 to the visitors. He cooly finished a rebounded shot after defender Semi Ajayi almost scored an own goal.
Three minutes later, the Frenchman quickly bagged his second, converting his easiest chance of the evening as Tierney angled a cross straight onto his right foot. The embarrassment the Baggies were trying to avoid was starting to look very real.
Arsenal went on to smother the hosts for the rest of the match, Johnstone being called into action a couple more times to make up for some dire defending, notably saving a powerful shot by Aubameyang in the final 10 minutes.
The future is bright for Arsenal
Arteta's men have now taken 9 points from their last three games as their newly tweaked young side continue to give their boss the winning formula.
Back to back clean sheets for the Gunners' further shows their improvement as of recent. The manager is starting to repay the faith shown in him by the club, winning two away matches in the space of a week.
Lacazette was back to his best today, scoring twice in a dominant attacking performance. He was crucial to letting the play flow up front and elevating the game of Smith-Rowe and Saka, who were playing just off the number 9.
Arsenal now move up to 11th in the table.
West Brom looking unmotivated under Allardyce
West Brom have now conceded 17 goals in their last four home matches, seeing them deservedly drop to 19th in the table.
BT Sport's pundits suggested that the new manager may now regret his appointment as new Baggies boss, as his deep defending and counter attacking style of play does not seem to be working out for the Midlands side.
Fans are unlikely to be hopeful for their next game away at Wolves, as this newly promoted team has scored only one goal in their last three games.
Star player- Kieran Tierney
The left back scored and assisted a goal in Arsenal's most impressive win this season. He has looked so reliable when starting for the Gunners since joining from Celtic at the beginning of last season.
Tierney told BT that he was "delighted" to score, as his opener replicated that of a striker's finish.