Lampard and Bielsa have had a rivalry that dates all the way back to the former's time at Derby County, when the Leeds manager admitted to spying on other Championship teams to try and gain a tactical advantage.
In the end, there was a lot of fight and passion from both sets of players but there wasn't too much drama this time around. It was another comfortable win on the door for Lampard.
Story of the match
Everton made four changes from the midweek defeat to Newcastle United. Yerry Mina, Andre Gomes, Andros Townsend and Demarai Gray came out for Jonjoe Kenny, Donny van de Beek, Alex Iwobi and Dominic Calvert-Lewin coming in.
By contrast, Leeds were unchanged from their enthralling 3-3 draw against Aston Villa on Wednesday night.
The hosts made a bright start with a high-intense opening reminiscent of their change in style under Lampard.
On the other hand, the visitors suffered a blow with less than 10 minutes on the clock when Stuart Dallas had to be replaced by 18-year-old Leo Hjelde.
That blow was doubled-down shortly after as Everton made their strong start count with a goal.
The home team worked an intricate move in the final-third and Leeds struggled to deal with the threat of Calvert-Lewin as Anthony Gordon launched a ball into his path. Diego Llorente could only knock the ball into the air and the on-rushing Seamus Coleman managed to divert it past Illan Meslier.
Leeds looked for a swift response and nearly got it in spectacular fashion when Rodrigo hit the cross-bar with a stunning volley from 25-yards.
With the woodwork still shaking, Everton weren't willing to stand on ceremony and their forward-thinking desire was rewarded yet again.
Gordon’s out-swinging corner landed perfectly on the head of Michael Keane, who made no mistake with an emphatic finish past Meslier. Two goals ahead and we had barely reached the halfway point of the first-half!
Gordon was having another excellent match and his enticing cross almost caught the run of Calvert-Lewin.
Moments later, Iwobi’s curling short from the edge of the area sailed just wide.
Richarlison ought to have wrapped the game up on 40 minutes when the ball deflected enticingly for him in the middle of the box, but his shot was brilliantly blocked by young Hjelde.
Both teams had a habit of needlessly giving the ball away, however, it was Lampard’s men who were managing to shift the ball into more dangerous positions.
Indeed, Calvert-Lewin was the latest Toffee to get a good opening. Meslier, though, was quick down to his left to make a smart save.
On the stroke of half-time, Rodrigo again rattled the woodwork – this time the post with a well-placed strike from 25-yards.
Again, it was striking to note how many times both sets of players were surrendering possession. Bielsa and Lampard both like to press in numbers but neither would have been happy with the amount of ball losses after only just retrieving it. It was like watching dogs that just wanted to play fetch, at times!
The second period was largely bluster from both sets of teams but Gordon ensured that a fightback would not be put together as the game closed in on its final 10 minutes.
The academy talent inadvertently got a slight touch on Richarlison's low strike from just outside the box, angling the ball into the bottom left corner. .
Dele Alli – who came on for Calvert-Lewin earlier in the match – almost put the icing on the cake with an outside-of-the-boot effort that spun just wide of the far post.
Salomon Rondon – also fresh off the bench – thought he had found that illusive fourth goal but Meslier made an incredible save to turn his close-range volley over the bar.
Everton fans began to sing "Super Frank Lampard" in the knowledge that the game was all wrapped up. Goodison Park was rocking from the first whistle, in truth, and the atmosphere change from a few weeks ago could not have been more palpable.
It wasn't a vintage performance from the hosts but they gave it a good go and they were rewarded for positive play. Such attacking intent and desire had not been present under previous manager Rafael Benitez.
It is a result that eases relegation fears on the Merseyside outfit, while reminding Leeds that they still have work to do if they want to avoid a nervy end to the campaign.