The 34-year-old scored from the penalty spot, the Blues' third of the afternoon, after two Jon Walters' own goals, with Eden Hazard rounding off the scoring at the Britannia Stadium.
And Lampard believes it was vital for Chelsea to bounce back with a convincing performance following Wednesday's 2-0 Capital One Cup semi-final first leg defeat to Swansea.
"It was very important to get our attitude right for this one," the veteran said after the game. "It was a freezing cold day, it was blowy and Stoke have been unbelievable at home this year.
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"But we were right on our game today and barring the first 15 to 20 minutes when they put us under pressure, we completely dominated and were brilliant."
Chelsea face Southampton in the Premier League at Stamford Bridge on Wednesday before hosting Arsenal four days later.