Gloucester boss Bryan Redpath made two changes from the side beaten at home by Quins last weekend, recalling full-back Olly Morgan and No.8 Luke Narraway, while Leicester included Ben Youngs and Dan Cole among their replacements.
Tigers were put under early pressure when Burns made a sniping run. England captaincy candidate Tom Croft halted the danger when he pulled off a stunning tackle from behind, before Flood put Leicester ahead through an angled 13th-minute penalty.
Burns took only five minutes to land an equalising strike, and Gloucester established a degree of territorial control as the back trio of Narraway, Alasdair Strokosch and Akapusi Qera regularly made headway.
But Gloucester did not help themselves through a number of handling errors – wing Lesley Vainikolo was the chief culprit - with a second successful Burns penalty appearing to be scant reward for sustained pressure.
And after playing the opening 40 minutes with a strong breeze at their backs, Leicester were the happier team at the break despite trailing by three points.
Youngs then appeared for his first Premiership outing of the season, taking over from Sam Harrison, with Tigers rugby director Richard Cockerill clearly hoping he could inject snap and verve to a team needing an increased tempo.
Leicester thought they had scored only four minutes into the period, but television match official David Matthews contentiously ruled otherwise. Although Flood then kicked a second penalty, Leicester could feel slightly hard done by.
Leicester put together a slick attack that ended with Flood darting over to make amends for his narrow failure 15 minutes earlier.
Leicester deserved to be ahead, but it lasted barely two minutes as Gloucester prospered when Youngs attempted an ill-judged pass, Narraway caught it and then finished in style.
The game had moved up a gear, and Leicester responded to that setback in blistering fashion, courtesy of Tuilagi’s opportunism. The Samoan international charged down an attempted clearance by England hopeful Charlie Sharples, then reacted quickest to gather possession and sprint clear for his 11th try in 11 appearances against Gloucester.
Flood could not convert, but Leicester were back in front, the lead having changed hands three times during a hectic six-minute spell.
Redpath rang the changes in an attempt to rescue the game, yet Leicester successfully closed the game out, underpinned by Flood’s third penalty.