The Sussex all-rounder's belligerent 38 not out off just 13 balls propelled England to a total of 247 for six in an innings reduced by rain to 39 overs on Thursday. (Agencies)
And, on his former Surrey home ground, the Barbados-born Jordan took three wickets for 25 runs, including three for three in 12 balls.
Sri Lanka, chasing a target of 226 in 32 overs after a fresh downpour, never recovered and finished on 144 in 27.5 overs when Lasith Malinga was bowled by Ravi Bopara under the Oval floodlights.
England, now 1-0 up in this five-match series, quickly reduced Sri Lanka to 19 for two.
James Anderson struck fifth ball, with Sri Lanka yet to score a run, when he had Lahiru Thirimanne lbw before left-arm paceman Harry Gurney had Kumar Sangakkara playing on for eight.
Sri Lanka were 60 for two, in pursuit of a target of 259 in 39 overs, when rain stopped play for the second time in the match.
Come the resumption, Sri Lanka needed to score at nine an over and, unsurprisingly, lost wickets in the face of such a stiff run-rate.
Tillakaratne Dilshan slashed at Jordan and was caught on the third man boundary by Gary Ballance.
Mahela Jaywardene made a typically stylish 35 before chipping off-spinner James Tredwell to Eoin Morgan at short mid-wicket.
Dinesh Chandimal was caught behind off Jordan and three balls later Nuwan Kulasekara skyed the paceman to wicketkeeper Jos Buttler to leave Sri Lanka struggling at 108 for six. And England captain Alastair Cook, once labelled a "donkey" in the field by predecessor Michael Atherton, then took an excellent running catch to dismiss opposing skipper Angelo Mathews.
England were in trouble at 152 for five when Sri Lanka off-spinner Sachithra Senanayake took two wickets in seven balls to remove Ballance (64) and Bopara.
But England, as Sri Lanka had done in their nine-run Twenty20 win at The Oval on Tuesday, enjoyed a late flurry with the bat.
They struck 93 off the last seven overs, Jordan ending the innings with a straight six off Malinga.
'Slingshot' seamer Malinga, so often a threat, saw his eight wicketless overs cost 71 runs.
Earlier, England opener Ian Bell made a near run-a-ball 50 before he flicked Mathews straight to Malinga at short fine leg.
Bell's exit was the cue for the umpires to take the players off the field as a thunderstorm delayed play for two-and-a-half hours.
The series continues at north-east county Durham's Chester-le-Street headquarters on Sunday.
The Sussex all-rounder's belligerent 38 not out off just 13 balls propelled England to a total of 247 for six in an innings reduced by rain to 39 overs on Thursday.