Onuoha became the first opponent to score against Chelsea in the league at Stamford Bridge this season with a memorable goal just before halftime when he weaved past three Chelsea defenders and fired wide of goalkeeper Petr Cech.
Sunderland, beaten 7-2 at Chelsea last season, doubled their lead after 52 minutes when a brilliant move involving Welbeck and Jordan Henderson, called up to the England squad for the first time, found record signing Gyan who gave Cech no chance.
Welbeck added the third in the 87th minute after a rare mistake by Ashley Cole who overhit a backpass to Cech, completing one of the most unexpected scorelines of the season.
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The upset left champions Chelsea, who were without first-choice centre-backs John Terry and Alex, top of the table on 28 points, two ahead of Arsenal who won 2-1 at Everton.
Manchester United, who fought back to draw 2-2 at Aston Villa on Saturday after trailing 2-0, are third on 25 points.
Sunderland moved up to sixth after ending a run of 11 successive defeats by Chelsea dating back to 2001.
