They will win the league with victory over Crystal Palace at Stamford Bridge on Sunday following a 3-1 success at Leicester on Wednesday.
But Chelsea needed a half-time rallying call to come from behind following a sloppy first half and Marc Albrighton's opener at the King Power Stadium.
Drogba, John Terry and Ramires scored to move Mourinho's side 13 points clear of Manchester City and Arsenal.
And Drogba, who levelled just three minutes after the break, admitted they needed some strong words to help them recover.
"A lot of things (were said), a few things you don't want to hear but a few things which were very good for us to hear," he told Chelsea TV.
"You could see in the second half there was a change, a reaction, and that was the goal of the speech, to create a reaction.
"It's important to show the way and show reactions and I'm really happy I managed to do it.
"The game didn't look good in the first half, the way we played and started
We are really happy with three good goals, we played very well in the second half."
Petr Cech replaced Thibaut Courtois in goal with the Belgium international failing to shake off a hip injury.
Cech, 32, has won the title three times with Chelsea and is eager to clinch another in front of their home fans at the weekend.
"This team has a very good balance, that's why everything is working and we have overcome difficult moments this season so hopefully we can wrap it up at home," Cech said.
"It's amazing when you win a title but if you win it at home it puts the icing on the cake."
Defeat ended Leicester's four-match winning run and they are a point above the relegation zone ahead of Saturday's visit of Newcastle.
Robert Huth (calf) and Andy King (hamstring) are doubts for the Magpies clash after being forced off in the first half.
"King doesn't come off unless there is something wrong, Huth likewise" said boss Nigel Pearson, who was involved in a bizarre post-match spat with a journalist when he called him "an ostrich".
"They have got to be doubts (for Newcastle)
Until we know the extent of the injuries it is very difficult to give an answer."
Source : PA
Source: PA