Just seven minutes remained when Shrewsbury winger Jon Taylor was sent off for handling Matt Doherty's header on the line, with Sako blasting home the resulting spot-kick.
Shrewsbury took the game to Wolves in the first Football League meeting between the clubs for 28 years, with the visitors indebted to goalkeeper Carl Ikeme for two sharp early saves.
Ikeme did well to keep out Taylor's close-range volley and then had to be alert to deal with a long-range effort from Ryan Woods.
Adam Reach also fired narrowly side as Shrewsbury continued to push forward, but Wolves also had their moments with the lively Sako involved in many of their better moves.
Sako's 20-yard drive forced a flying save from Chris Weale, who was then relieved to see Bjorn Sigurdarson's header come back off a post.
Shrewsbury continued to create chances in the second half, Curtis Main somehow ballooning over from close range after an inviting cross from Taylor while Luke Summerfield was also just off target with a header.
But Wolves snatched the three points thanks to Sako's late penalty to leave most of a 9,510 record crowd at the Greenhous Meadow disappointed.