But Bath scored four tries of their own, including a dramatic score by their captain Francois Louw with four minutes remaining which secured their bonus-point victory.
Tigers welcomed back fit again Tom Youngs, Geoff Parling and Croft to the pack after they missed the home game with Wasps. Croft was joined in the back row by Thomas Waldrom, Steve Mafi started in the second row and Matt Smith came in on the wing.
The sun was shining and with a firm pitch, conditions at a sold-out The Rec were perfect for running rugby which was underlined in a pulsating opening half.
A huge up-and-under by Flood took Tigers into Bath half for the first time and when Ollie Devoto knocked on Smith collected possession for Croft to make ground down the right. Eventually, a Bath offside in midfield gave Flood a simple penalty to give Leicester an early lead.
Mafi knocked on the restart, which was collected by Parling in an offside position but Stephen Donald pulled his penalty across the posts.
Donald made amends by playing a big part in the opening try of the game. His charge gave Bath momentum and took them into the Leicester 22 before Manu Tuilagi produced an excellent tackle to stop Rob Webber just short of the line. Bath recycled possession for Simon Taylor to crash over from close range. With Donald receiving treatment following his contribution to the try, Devoto took over kicking duties and added the extras to put Bath 7-3 ahead.
Tigers struck back with their opening try in the 13th minute. Ben Youngs' clever pass put Croft through a gap between front row forwards Webber and David Wilson before he rounded last man Devoto to score by the posts. Flood's conversion gave Tigers a 10-7 lead.
Tigers threatened again four minutes later when Mafi span out of Francois Louw's tackle on halfway. An overlap appeared to develop on the left but Semesa Rokoduguni intercepted Tait's pass and had a free run to the line for Bath's second try. It went unconverted as Bath held a 12-10 lead.
Tigers took the lead for the third time in the opening quarter when Flood landed a penalty from the right.
And Ben Youngs extended the lead in the 25th minute with a sensational solo try. He caught Bath napping with a tap penalty 5m inside his own 22 and by the time the home players reacted he had passed halfway and rounded Devoto to score his sixth try of the season. Flood added the conversion to put Tigers 20-12 ahead.
At the other end, Mafi was pinged for not rolling at the back of a ruck but Donald was again wide with his kick.
Tigers thought they had scored a third try when Thompstone latched onto Tait's pass and Smith dotted down, however, it was disallowed after the television match official ruled Tait's ball had gone forward.
Instead, it was Bath who grabbed the next score through Horacio Agulla on the stroke of half-time. Donald, with the advantage of a penalty, picked out Agulla with a crossfield kick and the former Tigers winged stepped around Tait to score at the left corner. Donald added the extras to leave Tigers 20-19 ahead at the break.
Bath began the second period on the front foot with Rokoduguni almost breaking through at the back of a lineout before Donald's grubber was collected by Thompstone close to his own line sparking a Tigers counterattack. Tuilagi's run took him past two defenders and into the Bath half but Tait knocked on bringing the attack to an end.
Donald's kick deep from halfway went dead ni-goal with the home support claiming it was helped on its way by Tait. Tigers then won a penalty at the resulting scrum, which was knocked over by Flood for the first points of the half in the 49th minute.
A high tackle on replacement lock Ed Slater gave Flood another penalty four minutes later, which he knocked over to extend Leicester's lead to 26-19.
Tom Heathcote, on as a replacement for Ben Williams, reduced the lead by three points after Dan Cole failed to roll at a ruck.
And Tuilagi produced excellent tackles on Eastmond and Agulla in quick succession to repel Bath attacks on the Leicester 22. Bath created an overlap on the right where Croft came across to stop Rokoduguni 8m out before Eastmond knocked on to relieve the pressure.
Heathcote missed the chance to cut Tigers' lead to one point with 13 minutes remaining when his 40m penalty struck a post and rebounded to Croft.
Bath had plenty of the possession and territory as the game entered the final 10 minutes but they were unable to find a way through, underlined by a thumping tackle by Tuilagi on Agulla which took man and ball into touch.
Bbu the hosts eventually broke through with four minutes remaining. Replacement prop Anthony Perenise broke down the right and had Louw on his outside to score at the corner and give the hosts a 27-26 lead.
Tigers were unable to respond in a frantic finale as Bath held on for the win. The result leaves Tigers second in the Aviva Premiership table with one game remaining, at home to London Irish on May 4.