With just four points separating five teams at the bottom of the table, London Irish desperately needed a win on home soil to manoeuvre their way into the safety zone ahead of next weekend's league finale against Newcastle.
But head coach Gary Gold will now have to sweat it out alongside Leeds, Harlequins, Worcester and Northampton next Saturday.
Bath, who came so close to throwing away a golden opportunity may, however, have booked their passport into the Zurich Premiership play-off.
The west country side move ahead of Sale Sharks on the League ladder and now just trail Wasps and Leicester.
But it all could have been a very different story.
London Irish look like they had done enough with a 72nd minute penalty but a wayward pass by young wing Delon Armitage handed Malone the chance to strike at goal and he did just that.
Bath, however, started the game in a ferocious fashion crawling all over London Irish in the opening 10 minutes.
The Exiles were forced onto the defensive and soon enough they cracked with wing Frikkie Welsh pouncing on a pass from Malone on the left wing.
England's Ollie Barkley struck the conversion but Bath were lucky to not find themselves trailing after the west country side conceded three careless penalties in as many minutes.
However, fly-half Barry Everitt first hit the posts, then missed the target before finally registering three points on his third attempt.
Everitt was on-song with his next effort after the sin-binning of Bath flanker James Scaysbrook, but Bath stayed 10-6 up thanks to a Malone drop-goal on 34 minutes, despite the earlier loss of England prop Matt Stevens.
That was until the Exiles took a morale boosting 13-10 lead into the break.
This time it was the turn of London Irish to throw Bath onto the back foot and they did just that in style.
First Armitage found room on the right wing before offloading to skipper Ryan Strudwick.
The South African lock was brought down but Paul Hodgson soon set full-back Michael Horak loose who, surprised to find space in Bath's defence, started his way over the line for a converted try.
However, London Irish could not maintain their advantage after the restart with Bath's Zak Feau'nati finding the try-line with a well-worked score which passed through several phases before the number eight swooped on a pass from Tom Cheeseman.
Barkley missed the conversion but later added a 60th minute penalty.
Everitt came to London Irish's rescue though with three penalties in 12 minutes to again turn the tables and take the side into a 19-18 lead until Armitage's wayward pass gave Bath a crucial scrum five metres from their tryline.
Bath could not get over the line to touch down but Malone slotted home an 84th-minute drop-goal before referee Ashley Rawden blew the final whistle.
For London Irish:Tries: HorakCons: EverittPens: Everitt 4
For Bath:Tries: Welsh, Fea'unatiCons: BarkleyPens: BarkleyDrops: Malone 2