Roy Hodgson’s side made it six wins out of six since their disappointing World Cup showing in Brazil, by beating the ‘Auld Enemy’ in their own backyard.
The Arsenal forward opened the scoring, heading home an inch perfect cross from Gunners team-mate Jack Wilshere.
Rooney scored his first of the night just after the restart when Scotland failed to clear an England free-kick. The Manchester United striker reacted quickest to head past Craig Gordon.
Andrew Robertson gave the home side hope when he fired low past Fraser Forster, who replaced Joe Hart in the England goal, but Rooney struck again to give the visitors a two-goal cushion.
Rickie Lambert and Adam Lallana worked well down the right and the latter picked out Rooney, in the middle, who made no mistake to score his 46th international goal.