Ruben Neves' wonderful strike in the ninth minute opened the scoring for the hosts before Ademola Lookman equalised for the Foxes.
Brendan Rodgers' side enjoyed the majority of the possession but couldn't break down a resolute Wolves defence before Daniel Podence struck a low effort into the bottom corner to make it back-to-back victories for the Wanders.
Victory is also Wolves' first win over Leicester in their last five top-flight games.
Story of the match
A fixture that is well-known for its lack of goals, three of the previous five meetings have ended 0-0, both sides entered the game in contrasting form.
Wolves came into the game with only one win in their previous five games, whilst the Foxes had failed to pick up three points in their previous four league matches.
Leicesters recent woes continued early in the contest when a piece of magic by midfielder Neves opened the scoring.
Lage's side could have extended their lead on a number of occasions at Molineux.
Brendan Rodgers' side, who were winless in their previous eight away games, grew in confidence as the game ticked on and found an equaliser through Lookman.
Youri Tielemans' threaded pass behind the Wolves defence allowed Albrighton the room to square the ball for the on-loan winger to tap in his sixth goal in all competitions.
The Foxes, who continued their unwanted run of 18 league away fixtures without a clean sheet, slowly became the stronger team in the early stages of the second half.
In the 59th minute, Lookman nearly doubled his tally with a wavy run through the Wanderers defence, but his side-footed shot was weak and Jose Sa was comfortable in the save.
Leicester's second-period dominance continued and spaces in Wolves' half continued. Lookman's brilliant cross fell to Tielemans, but the Belgium international side-footed his effort over.
Against the run of play, the home side restored their lead through another piece of excellence outside the box.
Ait-Nouri's tricky run down the left opened up gaps in the Leicester defence and Leander Dendoncker laid the ball off for Podence to fire into the bottom corner.
Maddison, who was forced off after feeling unwell in Thursday's win over Randers, was presented with a golden chance in the final 10 minutes.
A low cross from the left was dragged back to Maddison and the attacker got it all wrong and his strike went wide.
Pedro Neto, who had been out since April, was greeted with a standing ovation when he replaced Podence.
Leicester seemed to run out of energy after falling behind, failing to test Sa in the closing stages as their uninspiring season continues.