The sides were locked at 10-10 at the break, ex-New Zealand centre Laulala going over for the Blues while full-back Burns crossed for the Cherry and Whites. Blair and Robinson also kicked five points apiece.
But a hat-trick from Simpson-Daniel put the visitors out of sight, meaning Sweeney's late try was little consolation for Dai Young's side.
Some ill-advised adventure from the home side allowed Gloucester to level the scores on the stroke of half-time.
Sweeney looked to move the ball wide with a cut-out pass but it was picked off by Burns who sauntered over and Robinson converted.
Gloucester carried that momentum into the second half and after Ben White was sin-binned for slowing down the ball, they moved the ball right after a quick-tap penalty for Simpson-Daniel to score and Robinson converted from the touchline.
The Blues responded with a spell of pressure of their own and Blair kicked his second penalty to narrow the deficit to 13-17.
But that was as close as the hosts got as flanker Akapusi Qera fed Simpson-Daniel for his second, and a Burns chip then gave the ex-England wing his treble.
Good work from Laulala put Sweeney in for a try two minutes from time. But it was not enough for the Blues, who now face a battle for Heineken Cup qualification through the Magners League.
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