Ibrahimovic moved onto 50 goals from 99 games, surpassing Rydell’s haul of 49 from just 43 games.
The Sweden captain grabbed his first after just three minutes, although replays suggested the ball may not have crossed the line, before adding a second shortly before the half-hour with an improvised flick.
The 32-year-old, who had been doubtful for the match because of a throat problem, was given a rapturous ovation by the 15,421-strong crowd in the Friends Arena when he left the field just after the hour mark as Sweden claimed a 2-0 win.
Rydell's tally had stood since 1912.
"That it was with a back-heel was probably a little lucky but it was the only way I could score," a beaming Ibrahimovic told reporters.
Asked which of the 50 goals was his favourite, Ibrahimovic chose his stunning scissors-kick from 30 metres against England in a friendly in November 2012.
"The most beautiful was against England, no one's going to beat that, but all goals are important," he said.
Ibrahimovic credited Russia coach Fabio Capello with turning him from a player with potential into a top marksman during their time together at Juventus.
"When I met Capello that's when I became a goal-scorer. Before that I played to play well, then I realised that goals are important," he added.
- Sports & Recreation