The midfielder volleyed in from close range to chalk up his second goal of the season and give Blues three big points.
Freddie Sears went close for Town in the first-half and Cole Skuse was denied by the post and an excellent save from Ben Amos after the break but Tabb’s strike was enough to separate the teams.
Town made one change to the side that went down at Middlesbrough at the weekend, Bart Bialkowski in goal for the injured Dean Gerken.
Jonathan Parr volleyed over after a corner had landed at his feet on the edge of the box in the first opening, the Norway international then putting too much on a cross for Tabb.
Bialkowski beat out an effort from Giles Coke after Eidur Gudjohnsen had found him 20 yards out, then Blues had a gilt edged chance to open the scoring just past the quarter hour when Sears robbed Tim Ream and raced clear on goal but Amos was equal to the task.
Sears fizzed in a cross that just evaded Daryl Murphy, then Craig Davies escaped down the flank but his shot drifted wide of the far post with Gudjohnsen lurking.
A surging run from Tyrone Mings almost saw the defender convert after he exchanged passes with Sears, then Bolton broke in the same move and Christophe Berra had to time his challenge on Gudjohnsen.
Town were inches away from going ahead on the half hour, Berra met a free-kick but Tommy Smith couldn’t force the ball over the line at full stretch.
Gudjohnsen saw a shot deflected wide after Josh Vela had fed the ball back into the danger area, then Parr cleared off the line from Ream as the deadlock threatened to be broken at both ends.
Tabb fired straight at Amos as the Bolton defence parted but Wanderers had an even better chance to open the scoring when the impressive Diogo Rochinha swapped passes with Davies but his finish from close range was a foot wide of the far post.
Luke Varney replaced Parr at the break in Town’s first change, Smith doing well to deny Davies inside the Blues box as the second-half got underway.
Luke Chambers sent a left foot effort wide before Blues made a second change with Kevin Bru introduced for Bishop.
The midfielder was close to making an immediate impact, his cross looked destined for Murphy until Amos ended the danger.
Skuse’s dipping volley landed on the roof of the net after Sears was prominent in the build up, Skuse then seeing his shot cannon back off the post and his follow up saved well by Amos.
Murphy spun away from his marker but dragged his shot wide as Town pressed for that vital opening goal and it finally came 10 minutes from time, Tabb’s volley finding the net from 12 yards out.
Bialkowski saved comfortably from substitute Rob Hall, Bru lashing a low drive just wide of the far post as Blues looked to wrap up the points.
Davies had one last chance to rescue a point for the visitors but he sent his header into the sidenetting as Town held on for the three points.