The West Indies had survived the first 10 overs of the day when Onions, whose first innings haul included three wickets in an over, had Lendl Simmons (21) held behind square by Cook.
Then, for the second time in the match, Swann had Shivnarine Chanderpaul, currently ranked as the world's number one batsman, out cheaply.
The left-hander, who never looked comfortable against the ball turning away from him, did at least avoid the indignity of a pair.
But he'd made just four when he pushed forward uncertainly against Swann and gave a bat-pad catch to Bopara at silly point.
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