This was the third time this season that Crawley have beaten a top-of-the-table team following wins over Peterborough and Leyton Orient.
Wolves, who went into the game boasting 19 clean sheets, came under early pressure and defender Danny Batth was forced to block a goal-bound shot from skipper Josh Simpson.
Tubbs threatened with a dipping 25-yard effort which goalkeeper Carl Ikeme smartly turned over the crossbar.
Wolves went ahead after 25 minutes when James Henry struck with a deflected shot from 25 yards out which flew into the roof of the net off the outstretched leg of keeper Paul Jones.
But Crawley replied within a minute through Billy Clarke, who drove a sot past past Ikeme after being set up by Andy Drury.
The hosts went in front in the 32nd minute when Clarke found Tubbs in space 15 yards from goal and the striker gave Ikeme no chance with a clever chip for his seventh goal in eight games.
Henry shot wastefully over the bar six minutes before the break after substitute Leon Clarke was denied by Jones.
Jones did well again just after the interval to parry a goal-bound shot from Clarke, and later produced a similar save to thwart Bakary Sako.
Wolves struggled to find a way back into the game and Simpson came close to adding a third for Crawley late on.