A snap drop-goal from London Irish fly-half Barry Everitt after the 80-minute mark looked to have given the Exiles the points after a tension-filled end saw Bath fullback Matt Perry fluff a late touch-finder, but it was Seveali'i's heroics that might just keep Bath in the top flight.
The big Samoan was put away for the try after a lightning break by Wales scrum-half Gareth Cooper on the counter-attack, the West Country side winning a game which Irish dominated both in territory and possession, and which had looked like going the way of the visitors before a topsy-turvy end.
Bath are still facing down the barrel of the relegation gun at fourth-bottom in the table, but crucially they have played two more games than bottom side Newcastle Falcons, who visit the Rec on May 10, and are only two points behind coach Michael Foley's side.
Bath have also played one more than third-bottom London Irish who are one points behind them, and three more games than West Country rivals Bristol who are second bottom, and who host Bath at Ashton Gate on May 4 in a match with massive importance attached. Saracens are the other side in the equation at fifth-bottom, on the same points as Bath, but having played a game less.
Earlier in the game, two penalties from Everitt had put London Irish into a 6-0 lead on 36 minutes, before a penalty from Bath's Olly Barkley and a try from Irish centre Kevin Maggs – converted by Barkley – on the stroke of half-time gave the hosts a 10-6 interval lead.
Maggs profited after Exiles wing Paul Sackey botched a clearance, going over from a resulting close range scrum as the powerful midfield man bullocked into the post pads for the try, with lock Steve Borthwick in close attendance.
Irish were down despite dominating the opening period, and after a missed Mike Catt drop-goal attempt from long range for Bath, a third penalty for Everitt midway through the half land then another soon after looked like having won the day at 12-10 up and with 20 minutes to play.
Barkley slotted over his second penalty not long after to snatch back the lead, and after a frantic finale – where Catt again left the field with a hamstring injury – Everitt's quickfire drop-goal got the travelling support on their feet as it looked like they had snatched a dramatic win.
But that honour was to go to Bath in the end, and that man Seveali'i, whose support from a Cooper break saw veteran back rower Chris Sheasby rounded down the wing, Seveali'i waving the ball to the crowd before dotting it down for the try, the conversion attempt striking the woodwork and bouncing out.
For Bath:Tries: Maggs, Seveali'iCon: BarkleyPens: Barkley 2
For London Irish:Pens: Everitt 4DG: Everitt