With England having already qualified for next year's tournament, the stage was set for their captain to surpass Bobby Charlton's 45-year-old mark of 49, which he had equalled in Saturday's 6-0 win in San Marino.
After substitute Harry Kane broke the deadlock, the moment duly arrived in the 84th minute, Rooney crashing a penalty into Yann Sommer's top-right corner and being rewarded with a standing ovation that left him wiping away tears.
"I knew it was a big moment and just picked my corner and put my foot through it. To be the record scorer before the age of 30 is nothing I could have imagined."
Charlton, whose Manchester United record of 249 goals is also being eroded by Rooney, was quick to offer congratulations.
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"I would like to congratulate Wayne on becoming England's leading goal-scorer," the 77-year-old, emblem of England's 1966 World Cup win, said in a statement.
England manager Roy Hodgson said: "I'm delighted for Wayne Rooney and his breaking of the record, and showing such courage and ability to blast it into the roof of the net.
"His maturity has impressed me, the way he's accepted the captaincy. He's still out there working as hard as the 19- year-old making his way in the game."
Hodgson revealed that Rooney had been presented with a commemorative shirt by the Football Association and had made a short speech to his team-mates after the game.
There were also messages of congratulations from United and Gary Lineker, who had stood second behind Charlton on 48 goals prior to Rooney's goal against San Marino, which also came from the spot.
- Kane breaks deadlock -
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The result gave Hodgson's side an eighth consecutive win, keeping them on course to finish Group E with a perfect record ahead of October's final two qualifiers against Estonia and Lithuania.