It eased fan frustrations near the end of a disastrous season, which has seen Lampard make a surprise return as interim boss after Thomas Tuchel and Graham Potter's sackings.
But tensions were high before kick-off when travelling supporters booed Sterling and Ziyech when their names were read out.
Both players responded positively, registering an assist each for Benoit Badiashile and Joao Felix's decisive late goals.
And instead of urging Chelsea fans against booing their own players, Lampard hailed the visitors' following as "fantastic."
He told reporters at the Vitality Stadium: "Our fans were fantastic today. I appreciate their support.
Chelsea fans booed Raheem Sterling at Bournemouth. (Image: Getty)
"And we had a meeting at the end of the game on the pitch where everyone felt good for a day. It's important to feel that connection.
"In terms of the subs, they made an impact. Raheem was involved in a goal. Hakim gave us an assist. Opinions can always change, but they are two players that want to do well.
"There has been a lot of underperformance this year, but that's temporary. Their class is permanent, and they showed it."
Lampard has learned to celebrate the small successes during his woeful second stint in the Stamford Bridge dugout.
And he admitted he'd be enjoying a beer on Saturday night after tasting victory for the first time since his April return.
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