The Exiles move up to third in the table thanks to Geoff Appleford's second-half try and two late drop-goals from replacement fly-half Barry Everitt.
The Tykes enjoyed the lion's share of the possession and pressure, but Scotland star Gordon Ross had real trouble tuning-in his kicking radar, and three missed penalties let the Exiles off the hook.
With London Irish's injury worries finally abated, the return of back row men Kieron Dawson and Chris Sheasby helped the visitors soak up the home side's early raids.
The momentum was with Leeds however and, although poor handling was letting them down at crucial moments, Ross got lucky with his third penalty attempt to open the scoring in the 37th minute.
But, the Tykes' lead lasted only two minutes before Mark Mapletoft converted a place-kick to level the scores in time for the break.
Ross added another penalty early in the second half, but the Exiles responded by upping the tempo and Appleford soon crashed through three tackles for the game's first try – Mapletoft being only to happy to add the extra two points.
The visitors continued to press and Leeds were forced into killing the ball, but Mapletoft's ensuing penalty rebounded off the post.
Leeds acknowledged that they had been handed a 'get out of jail' card and immediately took the ball back up the pitch. They were soon rewarded with a penalty which Ross managed to slot to pull his side back 10-9 with 17 minutes remaining.
The Tykes thought they had scored the try which would have taken them into the lead when Matt Cardey appeared to touch down a loose ball, but referee Tony Spreadbury saw things differently and awarded a scrum.
Undaunted, Leeds kept the pressure up and soon won a penalty, but Ross missed the chance to take the Tykes in front.
Now it was the Exiles turn to appreciate the immense let-off, and appreciate it they did.
After rumbling up field, Everitt – on as a second-half substitute – dropped for goal with three minutes remaining to put the visitors four clear, he then immediately followed up with another strike to put the result beyond doubt.
For Leeds Tykes:Pens: Ross 3
For London Irish:Try: ApplefordCon: MapletoftPen: MapletoftDrops: Everitt 2