The Premier League leaders were held to a 1-1 draw at The Hawthorns in their previous top-flight fixture as Victor Anichebe popped up with an 87th-minute equalizer for the struggling hosts.
Chelsea looked set to drop points again on Saturday as Roberto Martinez's Everton held firm at Stamford Bridge while creating opportunities of its own.
Yet Mourinho's men made a vital breakthrough in injury time, fit-again captain John Terry being credited with the goal after challenging Everton goalkeeper Tim Howard from a Frank Lampard free-kick.
Reflecting on his side's dramatic triumph, Mourinho said: "The feeling when you lose points in the last minutes, like we lost two points against West Brom, is a bad feeling. When you win it's the opposite. It's basically a compensation of the points we lost against West Brom.
"'For the last 15 minutes we were strong, we create, we pressed, we dominated. When you score (a late goal) you can speak about luck ... but the reality is the boys chased that.
"A point for them (Everton) is good. A point for us is not good, and in the end maybe we deserved it."
Chelsea's triumph ensured that it will finish the weekend at the top of the Premier League table.
One negative for Chelsea was an injury that forced Oscar to be withdrawn at halftime.
"He said he could cope with the pain, there was no risk to make it worse, but he couldn't," Mourinho explained.