The Three Lions failed to break the deadlock after the opening 45 minutes at Wembley Stadium, but scored four times in the second half to claim a 4-1 win.
The result means that Roy Hodgson's side are now on the verge of reaching next year's tournament in Brazil.
"It was a game of patience," Welbeck told FATV. "We had to be patient with our play and keep the tempo up, make sure we do the right things.
"We had to be careful as well, as they have some players who could have caught us on the counter-attack. But early in the second half we got the goals and we were pleased with that."
England can book their place at the World Cup when they take on Poland at Wembley Stadium on Tuesday.