Rashid bamboozled Ireland's batsmen, taking 5-27 in eight overs, as the visitors slumped from 40/0 to 126 all out.
In reply, Alex Hales struck a brisk 55 and Joe Root an unbeaten 49 as England raced to their victory target in just 20 overs, according to an England and Wales Cricket Board (ECB) release.
Wickets started tumbling once Mark Wood, returning to England colours for the first time since September, bowled opener Paul Stirling for 20 after Ireland, winning the toss had raced to 40.
Joyce followed shortly after, missing a full and straight delivery from David Willey before Andy Balbirnie hit Jake Ball for successive boundaries as he and Porterfield put on 35 but the Notts fast bowler would have the last laugh, enticing an edge from the right-hander, Sam Billings taking a good catch behind the stumps.
Rashid and Root came into the attack and Ireland crumbled in the face of spin. Root struck first, Porterfield chipping to Liam Plunkett at mid off and then Rashid trapped both Gary Wilson and Kevin O'Brien in front to leave Ireland 104/6.
Stuart Thompson was next to go, bowled by a beautiful Rashid googly. Root got one to shoot on and trap George Dockrell in front before Rashid wrapped the innings up, dismissing Niall O'Brien and Tim Murtagh.
In reply, England survived a mini wobble early on. Jason Roy departed with the score on just one as he flicked uppishly to Dockrell off Peter Chase and then Murtagh dropped a return catch offered up by Hales with the opener yet to get off the mark.
But after that reprieve, Hales got into his flow, repeatedly smashing both Murtagh and Chase through the covers.
Hales brought up his half century but then fell for 55, top edging an attempted pulll off Chase, Porterfield taking a good catch in swirling wind.
Eoin Morgan went for 10, caught by Kevin O'Brien at long leg after failing to connect properly with a Chase bumper.
Root and Jonny Bairstow, fresh from a magnificent 174 against Durham in the Royal London One-Day Cup on Wednesday, ensured the players wouldn't go off for lunch before the game was decided, taking 17 off a Thompson to seal a seven-wicket win.
The series concludes at Lord's on Sunday, which is likely to be a sell out for what is Ireland's second appearance at the home of cricket.
Brief Scores: England 126 (Andy Balbirnie 30, Ed Joyce 23, Adil Rashid 5/27, Joe Root 2/9) lose to England 127/3 (Alex Hales 55, Joe Root 49 not out, Peter Chase 3/44) by 7 wickets.