Results around the country would have been enough to keep the Tykes up even if they had finished 6-3 down at the end of a tense battle but Holt's try five minutes into added time made sure.
Leeds' players were unaware of other goings on and replacement hooker Holt made sure when he barged his way over by the posts to complete a smash-and-grab raid that will leave Bath scratching their heads for weeks to come.
They had dominated the game and led with five minutes to go thanks to a Chris Malone drop-goal and an Olly Barkley penalty.
But they could not turn their pressure into points and paid for it when Gordon Ross added a late penalty and then gleefully converted Holt's try.
Never mind relegation and the play-offs – there was enough riding on this game already as Bath tried to make amends for their woefully flat Powergen Cup performance against Leeds two weeks earlier.
They were still without injured centre Andrew Higgins and lock Steve Borthwick, while Mike Tindall's complicated foot injury is taking longer than expected to heal.
Also out of action were Isaac Feaunati and Matt Stevens, forcing John Connolly to hand Gareth Delve his first start at number eight since December and bring in David Barnes at loose-head.
But how much Tykes had left in the tank after their bruising win over Harlequins in the week was open to question, particularly with Iain Balshaw and Tom Palmer still sidelined.
The weight of that expectation resulted in a turgid first-half as both sides struggled to hang on to the ball and promptly kicked away most of their decent possession.
Only Matt Perry sparkled out wide for Bath, who relied more on the kicking of Malone and Barkley to work their way downfield despite having most of the possession.
It took 17 minutes for Bath to create their first chance, the pack ploughing forward from a lineout and releasing the ball for Malone to stroke over a straight-forward drop-goal.
Then they had to wait until first-half injury time to score again, with Barkley drilling a penalty between the posts after Colm Rigney had dived over the wrong side of a ruck.
Leeds were similarly starved of the ball after the break and started to wilt as Bath found another gear.
Their best attacking spell of the game ended with Barkley's cross-kick narrowly eluding wing Frikkie Welsh with the line in his sights.
Leeds were still in bonus point territory but only just after Barkley was well wide with a 59th minute penalty shot and they needed a brilliant saving tackle from Tom Biggs on Welsh to keep Bath out going into the final quarter.
Despite their heroics of the last month and on Tuesday night, conceding another point would have been fatal.
Ross gave Leeds hope with a penalty five minutes from time. It might have been a vital kick had Barkley not missed a chance of his own in the fifth minute of injury time.
But they completed the mugging in the fifth minute of injury time with replacement hooker Holt crashing over under the posts and Ross converting to spark the celebrations.
For Bath:Pen: BarkleyDrop goal: Malone
For Leeds:Try: HoltCon: RossPen: Ross
Bath: 15 Matt Perry, 14 Andy Williams, 13 Tom Cheeseman, 12 Olly Barkley, 11 Frikkie Welsh, 10 Chris Malone, 9 Martyn Wood, 8 Gareth Delve, 7 James Scaysbrook, 6 Geraint Lewis, 5 Danny Grewcock, 4 James Hudson, 3 Duncan Bell, 2 Jonathan Humphreys (capt), 1 David Barnes.Replacements: 16 Lee Mears, 17 David Flatman, 18 Chris Goodman, 19 Rob Fidler, 20 Andy Higgins, 21 Nick Walshe, 22 Ryan Davis
Leeds Tykes: 15 Diego Albanese, 14 Andre Snyman, 13 Phil Christophers, 12 Chris Bell, 11 Tom Biggs, 10 Gordon Ross, 9 Alan Dickens, 8 Alix Popham, 7 Richard Parks, 6 Colm Rigney, 5 Scott Morgan, 4 Stuart Hooper (c), 3 Gavin Kerr, 2 Mark Regan, 1 Mike Shelley.Replacements: 16 Matt Holt, 17 Rob Rawlinson, 18 Jon Dunbar, 19 Dan Hyde, 20 Mark McMillen, 21 Craig McMullan, 22 David Rees
Referee: Steve LanderTouch judges: David Kurk, Huw Jones-WilliamsAssessor: Paul Bridgman