The youngster followed his Under 23 teammates Sam Greenwood and Charlie Cresswell onto the pitch as a spate of injuries forced Jesse Marsch into wholesale changes to his side at Molineux.
At 2-0 down, Leeds were chasing the game, though the dismissal of Jiménez was set to unbalance the home side as much as the visitors were disturbed by the loss of their preferred 'keeper.
Saving a couple of miscued goal kicks, Klaesson hardly put a foot wrong and was reliable when called upon to protect all three points after Luke Ayling scored his injury-time winner.
In the dying moments of the game, Hwang Hee Chan looked to equalise for Wolves by letting fly from outside the box, but 21-year-old Klaesson dived and parried the effort.
In the same phase of play, the ball was returned to the box where Francisco Trincão took a shot from close range, and again Klaesson was there to keep it out.
The former England striker explained that Klaesson's injury-time double-save showed ability beyond his years.
"Came on for his Premier League debut after Illan Meslier was taken off and made two world-class saves late on to help Leeds to a dramatic 3-2 win," Shearer said.
In his team of the week, Shearer also named Trincão, who stepped off the bench to assist Wolves' opener and double the hosts' lead with his first Premier League goal.
Whites boss Marsch was praised by Shearer after the American led his side to come from 2-0 down to claim a huge league win at Molineux.
"After a tough first half, Marsch’s Leeds came out firing in the second to produce a brilliant comeback victory," Shearer said.