Leicester's Toby Flood and Ulster's Ian Humphreys dominated most of the game with their kicking but the Tigers eventually pulled away to win.
For the most of the game the Irish province looked more than capable of causing an upset and will be disappointed not to have come away with at least a deserved bonus point.
Ulster took a second minute lead when Humphreys kicked a 55 metre penalty as the Tigers were penalised for offside following a poor up and under from Geordan Murphy.
The visitors continued to have the better of the opening exchanges but when Chris Henry was penalised for not releasing, Flood levelled the scores with a 50 metre penalty.
Within minutes Ulster were back ahead with another penalty from Humphreys and remained so as Flood missed with his next attempt.
However, this setback was the forerunner for Leicester to produce the first sustained period of pressure.
The Ulster defence was softened up by some good driving runs from Thomas Waldrom and Marcos Ayerza resulting in a Leicester penalty which Flood converted.
Neither side was able to produce any continuity to their play with constant disruption due to penalty awards.
Humphreys made it 9-6 after 20 minutes with another sweetly struck kick but once again Flood tied the scores after the Irish were penalised at a scrum.
There continued to be very little between the teams and Ulster were showing no signs of being overawed.
Their pack were meeting the Tigers head on with halfbacks Paul Marshall and Humphreys kicking astutely to pin back the hosts.
Roman Poite's whistle continued to be the dominant feature of a desperately poor first half which was briefly enlivened by one powerful run from Alesana Tuilagi, who was the first to threaten the try line.
The wing was hauled down by the combined efforts of Andrew Trimble and Simon Danielli and when Flood booted the ball into touch the half-time whistle was met with a chorus of boos.
The boos continued into the second half when early on Nevin Spence was penalised for taking Murphy as he was airborne.
There was little in it but a penalty was awarded which secured a platform for the Tigers.
Flood's penalty put his side ahead for the first time in the match and it should have been 12-12 but surprisingly Humphreys missed with by far his easiest kick.
An excellent kick and chase from the lively Marshall was the prelude for Ulster's best period of the match and a couple of strong runs from Darren Cave put the Tigers' line under threat.
The home defence held firm and a penalty for not releasing relieved the pressure.
Ben Youngs was introduced in an attempt to put some spark into the Tigers' game but the visitors looked the more likely try scorers as the game entered the final quarter.
Leicester raised their game to score the crucial try with 12 minutes to go.
From a ruck inside the Ulster 22, Flood gained possession to put in a clever grubber kick and Smith won the race for the touchdown.
Then with the final kick of the match the outside half was successful with his fifth penalty.
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