Mohamed Salah, on his full debut, and Willian scored either side of Frank Lampard's 250th club goal, which came in following up his saved penalty in the second half.
It was the response Mourinho - now unbeaten in 77 home Premier League matches - had demanded after criticising his players' inability to cope with Crystal Palace last weekend following a second successive away league loss.
"At home they feel more comfortable," Mourinho said. "(But) Premier League we play 19 matches away, 19 at home.
"If I go to a wedding I don't go in jeans. If I leave my house for a walk in Hyde Park, I don't go in a smoking (jacket).
"These boys, they have to be able to go away from home and to adapt to the situation. This takes time, let's go step by step.
"In football to be champions and to win titles you have to play in the sun, in the rain, in the cold, in the hot, small pitches, big pitches, direct football, possession football. You have to adapt."
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