Sarries were heading for victory at Vicarage Road when Tigers launched an astonishing 26-phase attack that ended with the Ireland full-back's goal.
Saracens last home defeat was to Exeter in October 2010, and their overall record over 52 weeks is 32 wins from 36 games.
The first set-piece after 58 seconds left Leicester down to 14 players. Lock Ed Slater was sin-binned following a mid-air clash that saw Saracens number eight Jackson Wray fall heavily to the ground. But Alex Goode's penalty attempt drifted just wide of the right hand post.
Inspired by Schalk Brits, Saracens took their game to a Leicester side armed with more of their regular Test stars than their hosts. And the pressure told in the 10th minute with Thomas Waldrom penalised for not releasing.
It was a simpler kick than his first, but Goode's second penalty attempt rebounded off the upright.
Leicester showed how it was done with their first shot at goal, awarded when Goode was tackled and failed to release. Toby Flood made no mistake with a spot-on kick after 12 minutes.
Saracens repeated attempts at counter-attacking failed, but then so did Flood's second attempt on goal,
a long-range effort after Carlos Nieto blocked Thomas Waldrom's challenge on Neil de Kock in the 22nd minute.
Manu Tuilagi sparked a storming attack, bursting two tackles to put Saracens on the back-foot. With Waldrom then Logovi'i Mulipola driving on, Saracens defended in depth, producing bit tackles.
Leicester sustained the pressure until Tuilagi was pinned down illegally and Flood doubled their lead on 26 minutes
Saracens produced a response worthy of reigning champions two minutes later. Brits snaffled a loose ball from a lineout and thundered towards the line before foxing the defence with a subtle offload that released scrum-half de Kock, who delivered a pacy finish. Goode converted.
To the anger of their management, Saracens promptly conceded a cheap penalty for twice ignoring referee Andrew Small's orders to retreat 10 metres. Flood completed his hat-trick of penalties.
Back came Saracens, Leicester went offside and this time Goode nailed the resultant penalty in the 36th minute - but it was Leicester who ended the half in front as Flood arrowed over a 40th-minute penalty after Saracens were deemed to have folded a scrum.
There was no let-up in the second half with Leicester shut out by defiant defence then two tackles required to prevent a try on the left by James Short.
Tuilagi then made a huge hit on Matt Stevens, referee Small deemed it offside and Goode fired Saracens back in front six minutes after the break.
And when Leicester were pinged for side-entry at the breakdown in the 51st minute, Goode kicked a fine goal from wide on the left.
Another bursting break by Tuilagi saw Leicester regain the lead in the 64th minute. Saracens managed to haul him down, but the ball was kept alive and Slater made amends for his early indiscretion by forcing the ball down under a pile of bodies.
Flood's attempted conversion sailed wide, before Leicester conceded a penalty on 75 minutes, collapsing a driving maul on the right. Goode, so anxious taking his first two penalties of the game, slammed it home from wide on the right.
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