Chris Woakes took six wickets for 17 runs and Stuart Broad 4-19 in an Ireland second innings that lasted just 15.4 overs.
The visitors had been set a seemingly modest 182 to win on the third day of a match scheduled for a maximum of four days rather than the usual five allocated to a Test.
But they ended up being bowled out for the seventh-lowest completed innings score in Test history and lowest since 1955 as their dreams of a maiden win in the format were blown away in a match in which they had dismissed England for 85 in the hosts’ first innings.
England, resuming on their overnight 303 for nine, saw their second innings end with the first ball of the third day’s play when debutant Olly Stone was bowled for a duck by Stuart Thompson.
Rain delayed the scheduled 10am (GMT) start by a few minutes but any hopes England had of adding to their overnight total evaporated when Thompson’s inswinger knocked over Stone’s leg stump.
Ireland had yet to give off the mark in their second innings when rain stopped play just seven balls into their chase.
They do, however, have two days in which to get the runs they require, with the Test scheduled for four days rather than the standard five.
Ireland were looking for their first Test win in just their third match in the format following defeats by Pakistan and Afghanistan.
They put themselves in a strong position by bowling England out for just 85 in the hosts’ first innings after veteran seamer Tim Murtagh took 5-13 on his Middlesex home ground and they then made 207 in reply.
One-day world champions England were indebted to nightwatchman Jack Leach’s 92 and Test debutant Jason Roy’s 72 before they suffered another worrying batting collapse just a week before the start of a five-match Ashes series against Australia at Edgbaston.