Scotland threatened a late comeback when Andy Robertson drilled home from inside the box in the 83rd minute, but Rooney netted his 46th international goal moments later to seal the victory.
Here, Sports Mole takes an in-depth look at whether the Three Lions deserved their win over their oldest rivals.
On target: 2
On target: 5
Was the result fair?
Yes. Plenty of people tipped Scotland to get something out of this game tonight due to their recent good performances under Gordon Strachan and the fact that they had home advantage. There were even questions whether England could match the hosts' hunger and desire, with the fixture seen by some as being more important to those North of the border.
However, England proved their doubters wrong and were well worth the victory in Glasgow this evening. The Scots may have had more of the ball, but they did very little with it and struggled to create many clear-cut chances. England's second goal right after half time was a real blow for the hosts and took the sting out of the game.
Even when Robertson raised hopes of a comeback with his late strike, that was quickly shut down as England responded perfectly by restoring their two-goal advantage. It was a good, entertaining affair, with the level of competitiveness you'd expect from this fixture, but England were comfortably the better side on the night.
Having held their own against the likes of Germany and Poland in recent months and beaten the Republic of Ireland in a barnstorming contest last week, tonight's performance was a big disappointment. Perhaps the Ireland game took a lot out of the hosts, who made just one change, but they were far short of their recent performance levels.
They were too sloppy in possession and gifted England the ball in some dangerous positions, particularly in the first half. At the other end they offered very little throughout, with Chris Martin, Steven Naismith and Stevie May getting hardly any joy against the likes of Gary Cahill, Chris Smalling and Phil Jagielka.
It should not be forgotten that Scotland's side was made up of a lot of Championship players tonight, while England boasted a full squad of Premier League stars. That gap in quality was evident, but nothing should be taken away from the work Strachan has done with Scotland since taking over.
Results have not been an issue for England since the World Cup, with tonight's victory making it six wins from six. However, performances have been concerning, which is why tonight's game will please Roy Hodgson as much as any of the competitive victories. This was arguably the best England have played for some time, and they were rewarded with a fairly comfortable win.
The Three Lions proved that they had the passion, hunger and desire to win the game, and on many occasions they outshone the Scotland players in that respect. The pressing off the ball forced a number of mistakes from the hosts, while they took control of possession much better than Strachan's side managed.
From the moment Oxlade-Chamberlain opened the scoring, it looked unlikely that England would relinquish their lead. Rooney's first goal came at an important time, while his second served to nip any Scotland fightback in the bud. It is another win for Hodgson's side, and this time they have a performance to be proud of as well.
Sports Mole's man of the match
Wayne Rooney: Just as on Saturday, Jack Wilshere deserves a mention here for another good display at the base of the diamond, but the award this time goes to Rooney. The skipper came up with two important goals at vital times in the match to ultimately guide his side to victory, while also working very hard off the ball to put the Scotland defence under pressure. He now has 46 international goals to his name, leaving him just three short of Sir Bobby Charlton's record. It is surely only a matter of time before he reaches that 50-goal mark.
There weren't many gaffes in today's game, so this one goes to Scotland's inability to clear their lines in the build-up to England's second goal. They had a couple of chances to get rid of the danger, but in the end Rooney was able to steer his header into the corner.
Jonas Eriksson dealt with what many expected to be a tricky fixture very well. There were a few rough challenges, as are to be expected in such a clash between rivals, but any flare-ups were quickly calmed down. He only went to his pocket once, when he had no choice but to book Charlie Mulgrew.
Scotland: Scotland are not in action again until March, when they will host minnows Gibraltar in a Euro 2016 qualifier.
England: England must also wait until March for their next match as they host Lithuania in a qualifier at Wembley.