The Liverpool striker netted his 20th goal in 28 games for club and country this season when he met Adam Lallana's cross at the far post in the 82nd minute, making a greater contribution in a central position than earlier on the left wing.
"It does not matter where I play on the field, it is about making a difference, making an impact," Sturridge said.
Although Sturridge had been repeatedly frustrated by goalkeeper Kasper Schmeichel's flurry of saves, the English display lacked urgency in the first half and they only just avoided a third straight Wembley game without scoring.
"I don't think we were effective as we wanted to be because we didn't get the ball forward quick enough," England coach Roy Hodgson said.
Although England seemed to be more effective after Rooney was replaced by Manchester United teammate Danny Welbeck on the hour, this display will hardly instil confidence that the team can provide much of a threat in the far hotter Brazilian climate.
"It would be too harsh to judge it on one performance," Hodgson said. "If we want to use all of these players together — and I thought we had a lot of talent on the field tonight — then there will be some work to do to make sure they gel together."
The biggest fear for Hodgson is losing a key player to injury before the opening match against Italy on June 14.
There was a scare early in the match when Daniel Agger's challenge caught Jack Wilshere's left ankle and the Arsenal midfielder's face showed he was in agony. But the stretcher was put away and Wilshere was able to continue playing until the 59th when he was replaced by Lallana.
England was in complete control — there was little for goalkeeper Joe Hart to do — but the dominance wasn't reflected by the goal threat. Even for a friendly, this was played at a slow pace by the hosts.
Rooney rarely looking like scoring, with the striker unable to get a touch when Sturridge sent in an inviting cross. But the final moments of the first half showed a sign of what was to come after the break, with Schmeichel making a sprawling save, booting away Sturridge's close-range strike.
"Unfortunately in the first half, our passing was not neat enough and a bit too slow, we did not get behind the opponents enough," Hodgson said.
Lallana was denied early in the second half by Schmeichel after being set up by Southampton teammate Luke Shaw, who came on to make his England debut.
Hart had to be alert to use his body to block Morten Rasmussen's effort before Schmeichel was called into action.
Schmeichel, who plays in the English second-tier for Leicester and is the son of former Manchester United great Peter, saved twice from Welbeck and pushed away Sturridge's curling shot.
But when Lallana cut in from the left and chipped the ball into the penalty area, Sturridge rose above Jesper Juelsgaard to head beyond Schmeichel.
The visitors, who qualified to qualify for the World Cup, didn't seem to rate England's chances.
"I wish you good luck in the World Cup," Olsen told English reporters. "You need it!"