Scholes then exploited excellent work by Manchester United team-mate Cole to score from close range.
Andy Cole ended his England goal drought as the revival under Sven Goran Eriksson gathered pace with a priceless win in Albania.
Cole struck England's third - his first international strike at the 13th attempt - as the battling Albanians were finally overcome in Tirana.
Swede Eriksson has breathed new life into England's World Cup hopes with victories against Finland and Albania in the space of four days.
Owen's strike stunned the resolute Albanians, and Paul Scholes added the second with six minutes to go to put England on course for a crucial victory.
England struggled to make any real impact for long periods against the rejuventated Albanians - but the result was everything and Eriksson will consider it a job well done.
Owen took advantage of a perfect pass from Scholes to score in the 73rd minute and cement the feelgood factor surrounding England since the arrival of new coach Eriksson.
Scholes then exploited excellent work by Manchester United team-mate Cole to score from close range.
Albania substitute Altin Rraklli was the benficiary of a mistake by Rio Ferdinand in injury time to give England an anxious last few minutes.
He also had a goal ruled out for offside in the dying seconds - but England survived and added that memorable third from Cole with virtually the last kick of the game to claim the points.
It now gives Group Nine a much more respectable look from England's point of view - although Germany remain in the ascendancy after their win in Greece.
Coach Eriksson sprang a selection surprise by giving an international debut to Arsenal youngster Ashley Cole.
And he was a prominent figure in a first half which saw England struggle to establish supremacy over a vastly-improved Albania side.
England suffered a blow after 28 minutes when influential defender Sol Campbell sustained an ankle injury in a challenge and had to be replaced by Manchester United's Wes Brown.
Beckham ended an England goal drought stretching to France 98 with the winner against Finland at Anfield - and was almost on the scoresheet again with a trademark free-kick.
Geri Cipi flattened Cole, and Beckham curled a shot around the Albanian wall to force goalkeeper Foto Strakosha into a spectacular diving save to his left.
And Strakosha was in action again to deny Beckham from another free-kick after Albania's Altin Lala was booked for a wild challenge on Ashley Cole.
England made a change during the interval, sending on powerful Liverpool striker Emile Heskey for Steve McManaman, who had been a peripheral figure.
And Heskey almost made an immediate impact as he deflected Scholes' cross narrowly wide after 48 minutes.
David Seaman had his first moment of anxiety after 54 minutes when a long range shot from Fatmir Vata reared off the turf, forcing England's veteran goalkeeper to save uncomfortably at the second attempt.
England had justifiable penalty claims waved away by referee Alain Hamer on the hour when Nicky Butt fell under challenge from Cipi, a decision that left captain Beckham, in particular, incensed.
Andy Cole was still struggling for that elusive first England goal, and he showed a lack of conviction as he got on the end of Gary Neville's cross but could not direct a weak header.
England finally broke the deadlock after 73 minutes, and it was in-form Owen who was the talisman again.
Neville started the good work with a raid down the right, and when Scholes threaded a glorious ball through to Owen, he provided the perfect finish to beat Strakosha.
England's second after 84 minutes was fashioned at Old Trafford and finished in Tirana as the victory was effectively sealed.
Andy Cole was creator with a surging run into the penalty area, and he provided an inviting cross for Scholes to score from inside the six-yard area.
Rraklli gave England a scare with an injury time strike for Albania after careless work by Ferdinand.
But Andy Cole cooled the nerves and boosted his confidence with a trademark penalty box swoop for England's third.
Albania: Strakosha, Lala, Xhumba, Cipi, Fakaj, Hasi, Fatmir Vata, Kola, Bellai, Alban Bushi, Tare. Subs: Beqaj, Rraklli, Muka, Duro, Skela, Dede, Fortuzi.
England: Seaman, Gary Neville, Campbell, Ferdinand, Ashley Cole, Beckham, Butt, Scholes, McManaman, Owen, Andy Cole. Subs: Phil Neville, Martyn, Brown, Carragher, Heskey, Sheringham, Fowler.
Referee: A Hamer (Luxembourg)