The Sussex paceman took a career-best five wickets for 29 runs as England, after fit-again captain Alastair Cook won the toss in overcast conditions, dismissed Sri Lanka in just 24 overs. (Agencies)
Cook (30 not out) and Ian Bell (41 not out), then made easy work of their meagre target, although left-hander Cook was dropped on 12 at square leg by Sachitra Senanayake.
Bell finished the day/night match with a straight six off left-arm spinner Rangana Herath as England, now 2-1 up in this five-match series, hit back just three days after being bowled out for 99 during Sri Lanka's 157-run win at Chester-le-Street.
The match took just 36.1 overs in total. Kumar Sangakkara top-scored for Sri Lanka with 13 in an innings where the only other batsmen to make it into double figures were Mahela Jayawardene (12) and skipper Angelo Mathews (11).
The tourists lost their last six wickets for nine runs in six overs.
Sri Lanka's total was their third lowest at this level, following the 43 they made against South Africa at Paarl in 2012 and 55 against the West Indies at Sharjah in 1986.
It was also their lowest in England, with their previous worst in the country also coming at Old Trafford when, as a non-Test nation, they made 86 against eventual champions the West Indies at the inaugural World Cup in 1975.
Heavy cloud cover favoured England's attack but conditions alone could not explain how Sri Lanka were bowled out with a mammoth 26 overs remaining.
James Anderson, on his Lancashire home ground, got England going with an opening burst of two wickets for no runs in five balls, with both Tillakaratne Dilshan and Lahiru Thirimanne caught behind by his county colleague Jos Buttler.
Dilshan was undone by an especially good delivery which cut back into him, Buttler taking a well-judged catch.
Sangakkara was caught behind off Jordan and the Sussex star then had Dinesh Chandimal taken at short extra-cover by Bell.
But it was off-spinner James Tredwell who, with his first ball, took the prize wicket of Jayawardene when the right-hander was plumb lbw on the back foot.
Mathews was then caught behind off Jordan, who in his 12th match at this level was well on the way to surpassing his previous best of three for 25 in England's series-opening 81-run win against Sri Lanka at The Oval last week.
The exit of Mathews was the cue for a flurry of wickets, that included a direct hit run out by Ravi Bopara.
Barbados-born Jordan, 25, appropriately wrapped up proceedings when he had last man Lasith Malinga lbw for two.
The series continues at Lord's on Saturday before concluding at Edgbaston on June 3.
The Sussex paceman took a career-best five wickets for 29 runs as England, after fit-again captain Alastair Cook won the toss in overcast conditions, dismissed Sri Lanka in just 24 overs.