Jordan's 4/6 saw off Windies for 45.
England won the T20I series after humbling the West Indies by a record 137 runs in the second cricket match on Friday.
An unchanged England made a mighty 182-6, with Sam Billings rescuing the side from 32-4 with a career-best 87 before he was out off the last ball.
The West Indies, debuting seamer Obed McCoy, was all out for 45 in less than 12 overs, giving England its biggest T20 victory.
Chris Jordan took four wickets for six runs to rip the heart out of the home side.
England, which lost the Test series and drew the one-day international series, won the T20s 2-0 before the third and final tour match on Sunday.
England was made to bat first, and Jonny Bairstow, Alex Hales, captain Eoin Morgan, and Joe Denly were gone after 5.2 overs.
However, Joe Root and Billings, the last two specialist batsmen, resisted. Root reached his first T20 half-century since 2016 off 36 balls. The two combined for 82 until Root was run out on 55 in the 16th over.
Billings compensated for running out Root by bashing the bowlers. He and David Willey, 13 not out, plundered 44 off the last two overs, evenly divided between Carlos Brathwaite and debutant McCoy.
Billings' 87 came off 47 balls, and included three sixes and 10 boundaries.
Willey and his left-arm medium pace started the West Indies' demise with two wickets in three balls, including the prized Chris Gayle first. Gayle scooped Willey's yorker to Root at mid-on, then Shai Hope was caught by Morgan after colliding with Tom Curran.
In the next over, Jordan took out Darren Bravo and Jason Holder in consecutive balls for ducks. The West Indies was 14-4, then 22-6 after Jordan's second over, where he dismissed Nicholas Pooran, who edged behind, and Fabian Allen, who edged to the slips. Both went for 1.
The mopping up was completed by Adil Rashid and Liam Plunkett, who finished with two wickets each.
(With AP Inputs)
