A trio of headers from Daniel Sturridge, Adam Lallana and Gary Cahill saw interim coach Gareth Southgate's side cruise home, the win consolidating England's leadership of Group F as they made it 10 points from four games.
Wayne Rooney, 31, started on the bench in England's last game, a 0-0 draw away to Slovenia, after losing his place in Manchester United's starting XI
Bastian Schweinsteiger and former Manchester United manager Alex Ferguson shook hands and shared a lengthy chat at Hampden Park, ahead of Germany's Euro 2016 qualifier against Scotland.
Thomas Mueller netted twice to help world champions Germany beat a spirited Scotland side 3-2.
The Scots slumped to a 1-0 defeat to Georgia in Tbilisi on Friday to deal a major blow to their chances of finishing in the top three spots in Group D.
Thomas Mueller gave the hosts an early lead in Frankfurt on Friday and Goetze scored twice as Germany avenged last year's 2-0 away defeat in Warsaw to replace Poland at the top of Group D.
World champions Germany were drawn alongside Czech Republic, Northern Ireland, Norway, Azerbaijan and San Marino.
Wayne Rooney's brace took the Manchester United striker clear of Jimmy Greaves, with whom he had previously shared third place, and left him three goals shy of Bobby Charlton's all-time record and two behind Gary Lineker.
Wayne Rooney became England's third-highest goal-scorer outright as Roy Hodgson's side defeated the Scots 3-1 to record a sixth successive victory. Elsewhere, Germany beat Spain and Portugal overcame Argentina by narrow one-nil margins.
Everton striker Steven Naismith believes Scotland manager Gordon Strachan will allow his side to play with more freedom against Georgia.