Everton thought they had a penalty when Yerry Mina went down in the box after a harsh challenge, the referee remained unfazed, and he waved play on, ignoring all the protests.
The game became a stop-start affair as both teams began to commit a lot of fouls. Youngster Anthony Gordon went on a mazy run before taking a shot from the edge of the box, but he saw his effort fly just wide.
Looking to score in back-to-back games, wingback Marcos Alonso received a good pass from the wing and fired a powerful shot at goal, but a brave block from the defender saw the ball bounce wide.
Everton started the second half energized, with Richarlison, in particular, looking to be a handful for the Chelsea defenders. Veteran fullback Cesar Azpilicueta suffered a lapse in concentration which allowed the Brazilian to steal the ball off him.
Richarlison picked up the ball and calmly slotted past Edouard Mendy in the Chelsea goal to give Lampard's men some much-needed breathing room.
The atmosphere in Goodison Park was magical and inspired by the first goal, fullback Vitali Mykolenko came close to doubling the lead, picking up the ball in space before firing narrowly wide from inside the penalty area.
Chelsea piled on the pressure, but all their efforts flew narrowly wide. At the hour mark, Mason Mount came close, smashing an effort from range against the post and looking to make amends Azpilicueta reacted quickly to try and convert the rebound, but Jordan Pickford made a great save.
Pickford was on hand again to brilliantly deny Antonio Rudiger's powerful header from the resulting corner.
For the second time in the game, Everton fans were unhappy with the officiating when Demarai Gray looked to be fouled in the box, but the referee immediately waved all the protests. A minute later, the ref waved away more protest when it looked as though Reece James handled the ball inside the penalty area.
Chelsea piled on the pressure, but Lampard's men remained resolute and wanted to preserve their lead at all costs. Super Eagles midfielder Alex Iwobi had a great game playing as a wingback.
The midfielder marshalled Marcos Alonso and put up impressive numbers playing in his ad-hoc role. Iwobi completed three defensive actions, won possession back four times, and contributed one key pass in another impressive performance under Frank Lampard.
Everton held on for their narrow win, but the three points still see them languishing in the relegation places, albeit with a game in hand over Leeds United in 17th.