The Tigers trailed by 17 points approaching half-time, but they out-gunned Gloucester after the break, ultimately claiming a bonus point win that keeps them firmly on course for a top-four finish with just three games left.
Tuilagi's double, plus touchdowns by his midfield partner Peter Betham, full-back Telusa Veainu and wing Vereniki Goneva's 74th-minute clincher ensured that Leicester triumphed in bonus point fashion, with fly-half Owen Williams kicking 10 points.
It was perhaps rough justice on Gloucester, who scored three tries during nine blistering first-half minutes from wing Steve McColl, centre Henry Trinder and prop Paddy McAllister, while skipper Greig Laidlaw kicked three penalties and three conversions for a 15-point haul.
But Leicester possessed just enough composure and experience to close out a pulsating contest as they kept in touch with Premiership top three Saracens, Exeter and Wasps.
Leicester handed a Premiership debut to 19-year-old flanker Will Evans, replacing Lachlan who failed a fitness test on his back, while prop Logovi'i Mulipola returned from suspension and Veainu lined up at full-back as Tigers targeted a key win in terms of their play-off bid.
Gloucester, on the back of three successive league defeats, made seven changes following last weekend's home loss against Bath, with number eight Ben Morgan featuring for the first time since mid-February and flanker Gareth Evans making his first start of the season.
And it was the visitors who struck first, courtesy of a fourth-minute Laidlaw penalty after a concerted spell of build-up play, but Leicester rapidly stirred and struck with two unconverted tries in quick succession.
Veainu pounced for the opener when he finished off a flowing handling move, then Tuilagi was on hand to touch down wide out after a beautifully-floated long pass from scrum-half Ben Youngs to Betham saw the Australian tap possession back inside to a supporting Tuilagi.
It was all too easy for Tigers, yet a second Laidlaw penalty clawed Gloucester back into contention, and then they capitalised on sloppy Leicester play to go ahead against the run of play.
Betham threw out a poor pass near Gloucester's 22, but it only succeeded in finding visiting fly-half James Hook, who ran 60 metres before finding McColl unmarked outside him, and he easily finished off.
Laidlaw's conversion made it 13-10, before Leicester imploded defensively as Trinder broke three tackles on a weaving run to the line as Gloucester's adventurous approach matched glorious weather conditions.
And matters deteriorated further for Leicester when McAllister powered over from close range as Gloucester continued to dominate, with Laidlaw's conversion opening up a 17-point advantage.
Williams kicked a penalty as half-time approached, yet Leicester could have few complaints following a second quarter implosion that saw them troop off 27-13 adrift.
Tigers boss Richard Cockerill made a double change at half-time, sending on flanker Brendon O'Connor and prop Marcos Ayerza, and Leicester did what they had to do by scoring first.
Williams made initial ground, and once the ball found itself in Tuilagi's grasp, he easily brushed off Gloucester's midfield defence to claim his second try, with Williams' conversion halving Gloucester's advantage.
A second Williams penalty meant that Leicester moved to within striking distance of their opponents, only for Gloucester to blow a gilt-edged attacking opportunity when their forwards pitched camp five metres from Tigers' line and hooker Darren Dawidiuk was penalised for stamping at a ruck.
Laidlaw then completed his penalty hat-trick as Gloucester hit 30 points, but back came Leicester when a superb midfield off-load from Tuilagi sent Betham over unopposed to set up a grandstand finale.
And Goneva came up trumps when he rounded off a thrilling handling move, sending a 22,000-strong crowd into raptures, before Tigers repelled a late Gloucester onslaught and emerged victorious following a thrilling tussle.