Jimenez slotted the ball through the legs of Toby Alderweireld and past Hugo Lloris in the 83rd minute, before Costa converted Matt Doherty's through-ball with three minutes of normal time remaining.
Harry Kane had put Spurs in front in the 22nd minute, when his spectacular long-range strike beat Rui Patricio for his 13th goal of the PL season.
But Willy Bolly headed in from Joao Moutinho's 72nd-minute corner before Wolves clinched victory.
The win moves Wolves up to seventh position on 29 points, while second-placed Spurs are six points adrift of leaders Liverpool, who play Arsenal in the day's late kick-off.
Spurs: 1 Jan v Cardiff (A)
Wolves: 2 Jan v Crystal Palace (H)