Chris Boyd's side scored six tries in all, with Tom Collins doubling up and Rory Hutchinson, Alex Mitchell, Fraser Dingwall and a penalty try bolstering the tally.
Dan Biggar added four conversions and Hutchinson one on an afternoon when Irish were hit by yellow cards for Rob Simmons and Nick Phipps.
The home side had gone into the game sitting five points above Saints in the Gallagher Premiership standings but the black, green and gold leapfrogged Irish with the convincing success.
Irish had gone 8-0 up early on but Saints scored twice in quick succession and then took the game away from their hosts during a sizzling second period in the sun.
Both sides were keen to play and it was to be Irish who struck first with a move that saw the ball moved quickly from right to left for Ollie Hassell-Collins to score in the corner.
Paddy Jackson missed the conversion but it was far from the start Saints had hoped for.
And Irish soon added to their tally, winning a scrum penalty in front of the posts to allow Jackson to make amends for his earlier miss.
Saints had a chance to counter soon after, and they flew forward only for Hutchinson to be stopped on the 22 as Irish scrambled well.
But Saints were starting to grow into the game and after Biggar booted a penalty to the corner, the away side scored.
Lewis Ludlam carried with real force before Hutchinson fired a lovely long pass out to Collins, who dived over in the corner.
Biggar converted and Saints soon scored again as Api Ratuniyarawa and Mitchell broke away before Hutchinson beat four players and rolled towards the line to ground the ball.
Biggar again converted well from the touchline and Saints led 14-8, having turned their fortunes around in quickfire fashion.
Irish needed to summon a response and a series of penalties inside the Saints half gave them a chance to do just that.
Jackson constantly turned down simple shots at goal to go for the corner, but Saints held out well.
Frustration was growing for Irish and that was emphasised when Simmons made contact with the head of Hutchinson at a breakdown, earning the Irish lock a yellow card.
It could easily have been a red as the shoulder made forceful contact, but referee Wayne Barnes deemed it a sin-binning and no more.
Saints held their six-point lead until half-time and they had two huge chances to extend their advantage as Courtnall Skosan and Ratuniyarawa both broke clear but were stopped at the last.
Finally though, the Irish resistance was broken as Saints put together a huge lineout drive before Phipps illegally ripped the ball from Sam Matavesi's grasp, earning the Irish No.9 a yellow card and handing Saints a penalty try.
It was soon to get even better for the black, green and gold as Skosan flew down the right and found the pass inside for the onrushing Mitchell to bag his side's bonus-point try.
Biggar converted and Saints led 28-8 with half an hour to go.
The air had been totally sucked out of the Irish balloon, and Saints were flying.
Dingwall delivered try number five after running a lovely line, allowing Biggar to make it 35-8 with the successful conversion.
Saints were in such a position of comfort that they opted to give their half-backs the final 25 minutes off, with Mitchell and Biggar replaced by Tom James and Tommy Freeman.
And Irish still had no response with Saints playing some sensational rugby.
The men in white soon delivered another eye-catching score as Collins spotted some space and chipped ahead before sprinting to the ball and getting there first to ground it.
Hutchinson added the extras and it was turning into the stuff of dreams for Saints.
There was one blow before the end as Skosan was forced off with what appeared to be a hamstring injury and, with the away side down to 14 men, Irish scored as Phipps went over.
The conversion was good but the gap was 27 points and Irish were just playing for pride in the final five minutes.
Furbank was yellow carded for a deliberate knock-on a couple of minutes from time, and Irish scored again through Phipps.
Jackson converted, but there was to be no bonus-point score for Irish as Saints played out the final few seconds before celebrating a sensational and significant away win.
London Irish: Stokes; Rowe (White 55), Cinti, van Rensburg, Hassell-Collins; Jackson, Phipps; Goodrick-Clarke, Creevy, Hoskins (Green 66); Munga (Mott 55), Simmons; Rogerson (c) (Pearson 55), Gonzalez, O’Brien (Cracknell 50).
Saints: Furbank; Skosan, Dingwall, Hutchinson (Litchfield 65), Collins; Biggar (Freeman 55), Mitchell (James 55); Waller (Auterac 55), Matavesi, Hill (Carey 60); Ribbans (Moon 58), Ratuniyarawa; Lawes (Haywood 66), Ludlam (c) (Coles 63), Augustus.
Referee: Wayne Barnes