Swann (five for 68) succeeded where England's seam attack did not initially, accounting for Essex's top three in the hosts' notional pursuit of 415 to win.
Then Graham Onions (four for 43) joined in, taking three wickets for no runs as as a rush of five went for 11 either side of tea to set Essex on the fast track to 186 all out and a 229-run defeat with almost 24 overs remaining.
This contest was widely reported as having descended into farce yesterday, when it lost its first-class status once Essex agreed to substitute two injured frontline bowlers with another of their own in Reece Topley and one England had rested in Boyd Rankin.
The intention was to make more of a match of it, after Ravi Bopara's bowling resources had been drastically depleted. But England's progress to 279 for four declared - including two batsmen who retired out, satisfied apparently with their preparations to face Australia next week - was still pretty serene.
They were able to call time at their leisure on their second innings, leaving themselves 73 overs to try to bowl Essex out. It seemed a mission improbable, on a good pitch which had nonetheless provided some turn throughout, especially while the seamers were drawing a blank in an opening stand of 91 between Jaik Mickleburgh (58) and Hamish Rutherford.
Swann did not make an immediate impact either and had to wait until his sixth over before Rutherford got greedy, missed a slog-sweep and was bowled off-stump by one that turned.
The off-spinner then made short work of Owais Shah, neatly caught at first slip by Jonathan Trott away to his left; then after Mickleburgh had reached his second half-century of the match, from 68 balls, he fell disappointingly when he clipped a low full toss straight to short midwicket.
Just before tea, Onions took the fourth wicket and his first when Bopara poked a tame catch to cover. Four wickets then fell in only 17 balls to Swann, and principally Onions.
First, Ben Foakes nicked one behind off Onions; then Mark Pettini moved up the pitch to Swann only to edge on to his pad to be caught at short-leg. There were two wickets in Onions' next over, Sajid Mahmood bowled middle-stump and Tom Craddock stuck on the crease lbw. David Masters was last out, caught in the deep off Swann, to end the innings with number 11 Tymal Mills unable to bat because of his strained hamstring.