Many had predicted a fiercely contested affair between the neighbouring nations but, despite some early resistance from the home side, goals from Alex Oxlade-Chamberlain and Rooney put Roy Hodgson's men in firm control.
The Arsenal midfielder's 32nd-minute opener owed much to a sublime assist from club colleague Jack Wilshere, who teed up the 21-year-old to head past goalkeeper David Marshall.
England's second shortly after the interval knocked the wind out of Scotland's sails at Celtic Park – Rooney this time on target with his head.
Andrew Robertson pulled one back out of the blue in the 83rd minute, but Rooney was on target again soon after to put paid to any lingering Scottish hopes.
Scotland brought Chris Martin in for injured striker Steven Fletcher, while Hodgson handed a first England appearance since 2012 to Stewart Downing, who was in the thick of the action early on.
The midfielder, occupying the central position in which he has excelled for West Ham this season, played in captain Rooney, who in turn fed Danny Welbeck for a strike that was unconvincingly stopped by Marshall.
Scotland, roared on by a fervent home crowd, settled after a period of English pressure, but both teams were struggling to carve out any clear-cut opportunities.
That was until the 32nd minute, when Oxlade-Chamberlain – one of six changes to the side that triumphed 3-1 over Slovenia in a Euro 2016 qualifier on Saturday – got his head to a pinpoint Wilshere ball into the area, applying the slightest of touches to beat Marshall.
England pressed for a swift second, but Welbeck was unable to control James Milner's pass in the centre of the penalty area as the move broke down, while Scotland's half ended without having tested Fraser Forster – the former Celtic stopper back on his old stomping ground.
Both managers elected to make changes at the interval, with Craig Gordon coming on to make his first Scotland outing since 2010, but his first task was to pick the ball out of the back of the net.
Robertson failed to clear his lines when the ball was driven into the penalty area by Wilshere, and Rooney reacted quickly to head beyond the reach of the current Celtic keeper, surpassing Jimmy Greaves to go outright third on the list of all-time England goalscorers.
Forster tipped over from a looping Russell Martin header at the other end as Scotland pushed to reduce the deficit, before Sheffield Wednesday frontman Stevie May was thrown on for his international debut.
Although Robertson did pull a goal back from close range seven minutes from time, Rooney found the net in similar fashion two minutes later - putting himself within two goals of second-placed Gary Lineker in the England record books.
