The former Derby County striker was Rushden and Diamonds' hero last month when they dumped City out of the FA Cup and Robinson looked to have marked his Walsall debut with another winner until Wetherall's late effort.
But the Saddlers were far from happy about his 82nd minute header which denied them a fourth successive league victory.
City were without injured marksman Dean Windass and their lightweight strike-force had rarely threatened until manager Colin Todd introduced on-loan recruit Owen Morrison who suddenly sparked a late rally.
After a sustained spell of pressure Morrison swung over a right-wing corner which was headed on by Steven Schumacher and Wetherall launched himself at the far post to force the ball home through a crowd of defenders.
Paul Merson's men disputed the goal with referee and linesman, but Wetherall's fourth of the season set up a frantic finale in which both sides wasted chances to claim the winner.
It was a dramatic turnaround to a low key contest which the Saddlers looked to have had in the bag.
Merson's men overcame the early loss of injured striker Matty Fryatt to dominated most of the game and Robinson's appearance off the bench spelled danger for City.
In a scrappy opening period Portuguese midfielder Jorge Leitao saw two great chances go begging thanks to a crucial tackle by Wetherall and then a great block by City keeper Paul Henderson.
Wetherall, who was impressive throughout, then blocked a Robinson strike before Bantams winger Nicky Summerbee wasted their best chance of the half with a miscued 20-yard shot.
City did manage to get the ball past keeper Joe Murphy at the start of the second half, but full-back Zigor Aranalde got back to clear Michael Symes' goal-bound shot and the Saddlers deservedly took the lead through Robinson's 61st minute finish.
Former England and Arsenal star Merson was at the heart of the move with his neat turn and pass, but Robinson was left unmarked to race in on goal and fire his right foot drive past Henderson from 10 yards.
Robinson should have bagged a second after Bradford failed to clear the danger, but his shot was saved well by Henderson and Walsall paid the price when Wetherall got on the end of Morrison's corner to salvage a point.