It was a huge win for the 18th placed Toffees in their quest to beat the drop as they closed the gap to Burnley and Leeds United, who are right above them, to just two points.
Everton do have a game in hand on their relegation rivals.
Lampard's status as a Chelsea legend did not deter him from enjoying the win and he was full of celebrations at Goodison Park after Richarlison's early second half strike gave them all three points.
With 211 goals, Lampard is Chelsea's record goalscorer but he hoped his former employers understand how much the win meant to him at this crucial moment.
“I have so much respect for Chelsea and the fans. So I hope they understand me getting excited with the win," Lampard told Sky Sports after the game.
“We needed it today, more than them. I have to be honest. For me, it was all about Everton today. Three points are so critical to us, when you see what it means to our fans’ lives.”
Everton's away form this season has been disastrous but under Lampard they have won six times in nine home games.
“The fans are in the middle of this. I am pleased the players could see on the way in what it means to the fans," he said.
“They know that and understand it. They got behind us, were nicely aggressive, this place has to be a hard place to come. Results have been good here at Goodison before I came, we have to maintain that.
“We have to fight for points, we are in the relegation zone and we have to go with that same spirit every game.
“They [the players] have to show they care. I like that. They don’t have to go over the line but have to show they care, the fans want to see that. I prodded them a bit before the game because the situation is clear. We need to perform with that level in all our remaining games. That needs to keep coming in and if it doesn’t we have to sort it out.”
