Having bowled out Ireland for 172 in their first innings, England effectively batted them out of the match when they declared on 524-4 with a massive lead of 352 runs after Ollie Pope and Ben Duckett made big centuries on Friday.
Resuming on 97-3, Harry Tector got Ireland off to a strong start, scoring 51 off 98 balls before holing out to point for debutant Tongue's fourth wicket of the innings.
Lorcan Tucker and Curtis Campher also departed before lunch to leave Ireland reeling, a third successive innings defeat seemingly inevitable after two heavy losses to Sri Lanka in April.
Andy McBrine and Mark Adair launched an effective counter-attack, however, in a blistering seventh-wicket stand, scoring 163 runs off 165 balls - the highest-ever test partnership for Ireland.
Matthew Potts broke the stand when Adair, on 88, got the slightest of touches on a delivery as it flew through to wicketkeeper Jonny Bairstow.
McBrine battled on after Fionn Hand became Tongue's fifth scalp, scoring 86 not out as he dragged Ireland over the line and forced the hosts to bat again, albeit briefly.
Chasing a paltry target of 11, England opener Zak Crawley hit Adair for three boundaries in four balls to seal England's 11th win in 13 tests.
"I think it gives us a good insight into the conditions and what we might get against Australia in the summer coming up," England captain Ben Stokes told the BBC.
"Ireland could have easily got further ahead of us with less time left in the game. So we gave ourselves that opportunity to bowl them out and not have to bat again.
"But fair play to Ireland, they batted really well there and we didn't have to go out and score many but it does prove that being ahead of the game as we were can really work in our favour when the pitch is as flat as that was."
England now shift focus to the Ashes series, which gets under way at Edgbaston on June 16th, after Australia's match against India in the world test championship at the Oval from June 7th.
England named an unchanged squad for the first two tests of the five-match series during the lunch break, with Tongue retaining his place after his impressive showing against Ireland.
