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A hugely-significant 1-0 win came courtesy of Richarlison's fourth goal in five matches and a brilliant second-half goalkeeping performance from Jordan Pickford.
Lampard's side have taken 10 points from the last 12 at home and a raucous Goodison, both outside before the game and inside throughout, will play a huge part in their future with two more home matches remaining.
Burnley and Leeds, with an inferior goal difference, are only two points away and Everton have a match in hand - at home to Crystal Palace three days before the final day of the season - so their destiny remains in their hands.
However, Lampard remains cautious.
- Everton 1-0 Chelsea - match report and highlights
- How the teams lined up | Match stats
- Premier League table | Fixtures | Results
Lampard: 'It's hard to say it's in our hands, long way to go'
"I don't know what is in your hands around the bottom of the table," the Everton boss added.
"If it was Liverpool and Manchester City you'd think they would win every game and then in your hands is great at that point. But are we expecting Burnley to win every game? At the minute maybe yeah! Are we expecting Leeds to win every game?
"It think it is hard to say what is in our hands and that's because we can only control certain things - and that's when we play.
"That's the difficult thing about yesterday, we can't control Burnley. We can't control Leeds. We can only control ourselves. Of the five games we will have to control ourselves well enough to get enough points. We don't know what that (total) is.
"My feeling is there is a long way to go."
Everton's remaining fixtures
May 7 - Leicester City (a)
May 11 - Watford (a)
May 15 - Brentford (a)
May 19 - Crystal Palace (h)
May 22 - Arsenal (a)
Lampard: We needed an extra boost
Ahead of the game, Lampard felt it was time to spell out the reality of the club's precarious situation to his players ahead of the visit of Chelsea and he was delighted with their response.
Burnley's surprise late comeback against Watford on Saturday had left Lampard's side five points adrift of safety heading into the game and the manager decided he needed to address it before they arrived at Goodison Park.
"I think it was an important moment to talk about the reality of the situation," he said.
"You can keep telling the players to believe. Then there are other times when the demands are this.
"To be good lads is not enough to stay in this league. It is clear what the table looks like.
"My feeling was we needed an extra boost, an extra bit of attention, and to be fair the players delivered that.
"I mentioned it (the Burnley result) briefly to the players this morning because I wanted to make sure it wasn't a fear or a lack of hope with the points difference."
Souness: Pickford won the game for Everton | Redknapp: It's save of the season
Richarlison may have grabbed the goal that sealed victory for Everton, but arguably more important on this occasion was the performance of Jordan Pickford, who after facing no shots on target for almost an hour, then produced an impromptu cameo to keep Chelsea at bay and the lead intact in the second half.
His superb denial of Cesar Azpilicueta, scrambling across his goal having been beaten by Mason Mount was the pick of the bunch and described by Sky Sports' Jamie Redknapp as the save of the season.
"The one to deny Azpilicueta is the save of the season, Redknapp said. "It was magnificent. We've given Pickford a lot of stick in the past, but he was brilliant."
Sky Sports' Graeme Souness added: "Jordan Pickford won the game for Everton single-handedly with his saves. Some of the saves he's not entitled to get anywhere near them."
Pickford: That's what I'm there for
Everton goalkeeper Jordan Pickford after his man of the match display:
"It is what I am there for, and it is a team effort at the end of the day, it is all about getting three points. I really enjoyed it but that is what I am there to do, help the team.
"We cannot get too carried away, we have to keep fighting and the fans have played a massive part."
Tuchel: What can I do about mistakes?
Chelsea boss Thomas Tuchel was left to bemoan another individual mistake - Cesar Azpilicueta losing possession on the edge of his own penalty area - which has left them anxiously looking over their shoulder in the race for a top-four place.
"What can I do? To give a goal away is the worst thing that can happen to you," he said.
"It is our responsibility. It happens too often. We struggle to play without big mistakes and that is why we struggle to have results.
"In the last few matches we struggled to have a clean sheet, the last four matches we have had one clean sheet.
"Very disappointed. We knew what was coming from the opponent: the crowd and the way they would approach the match. No one was surprised."
Chelsea's remaining fixtures
May 7 - Wolves (h)
May 11 - Leeds (a), live on Sky Sports
May 14 - Liverpool (n), FA Cup final
May 19 - Leicester City (h)
May 22 - Watford (h)
What's next?
Everton's next clash is a trip to Leicester City, before their crucial game in hand away at Watford on May 11. Frank Lampard's side end the season with home games against Brentford and Crystal Palace and then go to Arsenal on the final day of the season.
Chelsea host Wolves next weekend, before travelling to Leeds on May 11, live on Sky Sports, in their final match before their FA Cup final with Liverpool a few days later. The Blues then have home games against Leicester and Watford to end the season.