The Canaries were denied a 2-2 draw after Kenny McLean’s header was ruled out for offside.
After Jamie Vardy and Teemu Pukki had ended their respective goal droughts in the first half, a frantic second period produced more drama in Norfolk.
Daniel Farke’s men had looked the more likely to find a late winner but Albrighton punished the Canaries with a sucker-punch before celebrations by the hosts late on were cut short when Kenny McLean’s header was ruled out for offside.
Norwich had thrashed Bournemouth 6-0 in the Carabao Cup in midweek and the performance of Brandon Williams earned him a first league start.
Manchester United loanee Williams had only joined on Monday and was eager to improve with regular game-time, but was taught a lesson in how quickly mistakes are punished when the Foxes went ahead in the eighth minute.
After the left-back had tried to keep the ball in play, Ricardo Pereira stole it and raced past Ben Gibson to get to the byline where he cutback for Vardy to curl home the opener.
It was a trademark Leicester goal under Brendan Rodgers and an important strike for their number nine, his first on the road in eight months.
Joy quickly turned to anguish when the Foxes boss realised it would be Pereira’s last involvement after the full-back limped off following his assist.
Already without five defenders and the suspended Ayoze Perez, Rodgers turned to Timothy Castagne, who was back and in a face mask after a fractured eye socket cut short his Euro 2020.
Norwich did respond strongly to going behind with McLean and Todd Cantwell trying their luck before Caglar Soyuncu almost had another moment to forget.
The Turkish defender, at fault for West Ham’s opener on Monday with a wayward pass, again gave away possession and Kasper Schmeichel had to save his Leicester team-mate with a fine stop to deny Pierre Lees-Melou.
It was end-to-end now with Tim Krul required to thwart Vardy soon after before the leveller did arrive, yet only after a lengthy VAR check helped award the hosts a spot-kick.
Lees-Melou and Soyuncu were involved once more with the latter sliding in but referee Rob Jones awarded a corner before David Coote – in operation at Stockley Park – reviewed the incident and after nearly two minutes asked his fellow official to check the pitchside monitor.
Jones did not need long to change his mind and Pukki made no mistake with his penalty, ending a Premier League goal drought which lasted 15 games across two top-flight seasons.
Farke’s side had the momentum now and after Cantwell and Lees-Melou had fired off target, Pukki should have done better from Max Aarons’ perfectly weighted cross but the Finnish striker headed straight at Schmeichel.
FA Cup winners Leicester remained a threat and ex-Norwich midfielder James Maddison may have done better with two snap-shots from inside the area before Youri Tielemans sliced wide.
Rodgers has still seen enough and called for Kelechi Iheanacho with 23 minutes left and the substitute hand a hand in what proved to be the decisive goal.
Good work by the Nigeria international on the left found Maddison, who flicked into Vardy in space and he was able to find Albrighton on the opposite flank where the winger rifled into the bottom corner after a slight deflection off Williams.
It was cruel on Norwich but Carrow Road was celebrating three minutes later when McLean headed in Milot Rashica’s corner but with Cantwell standing in front of Schmeichel, VAR ruled the goal out for offside.
Substitutes Josh Sargent and Adam Idah both fired late opportunities wide to ensure injury-hit Leicester claimed all three points.