Welbeck doubled his personal tally in second-half stoppage time, slotting home from just inside the box to seal the points and give England a winning start to their Euro 2016 qualifying campaign.
Here, Sports Mole takes an in-depth look at whether the Three Lions were worthy victors at St Jakob Park.
On target: 3
On target: 5
Was the result fair?
On the balance of general play, it was a fairly even encounter this evening, but there is little doubt that England deserved their victory. The visitors created by far the better chances and, but for some poor decision-making in the final third and one inspired save, they could have won this match even more comfortably.
Switzerland had chances of their own and really started knocking on the door in the final 15 minutes of the match, but they rarely carried the same threat in the final third as their opponents did. They went into this match as favourites, but didn't put an England side low on confidence under enough pressure.
The hosts may have had more of the ball, but England used their possession more effectively than Switzerland did theirs. That was the major difference this evening as England created enough clear chances to finally take a couple, while the Swiss did not.
Not the ideal start for new boss Vladimir Petkovic, but he will know that easier tests are to come. Even so, he will look at this match as a missed opportunity given the fact that England arrived low on confidence after a poor summer and an uninspiring victory over Norway in their warm-up friendly.
The hosts did not do enough to force the issue this evening, rarely putting Roy Hodgson's side under enough pressure. They didn't approach the match as if they were the favourites, although they did create enough openings to feel that they should have at least scored. Josip Drmic in particular had a good chance, but he was denied by some superb defending from Gary Cahill.
All in all, there are positives and negatives for Petkovic to take from this defeat. His side showed bright moments, but were second best overall this evening. It was always going to be hard to follow Ottmar Hitzfeld, and this is not the start that the former Lazio manager would have wanted.
Much better. After a dull and drab affair at Wembley last week, Hodgson and his side came in for some intense criticism in the build-up to this game, but they responded well. It was by no means the perfect performance, but it was a vast improvement from their display against Norway.
The visitors were good in possession and should have been ahead at half time having squandered a few glorious chances. However, their decision-making and killer ball in the final third improved after the break, and that showed in the scoreline. It was a young side named by Hodgson once again, and this was a promising start to the campaign.
There were negatives to take from the display, but they were outweighed by the positives this time. The team will not need telling that there is still plenty of room for improvement, but right now they will be delighted to have come away from their toughest test of the group with three points and a clean sheet.
Sports Mole's man of the match
Danny Welbeck: There were a number of good displays from England this evening without anyone really standing out. The man of the match award, therefore, goes to the man who won the match for the visitors. Welbeck took his two goals well, showing different skills in converting on both occasions.
The striker did struggle with his first touch on occasions and wasted a great position with a poor pass in the first half, but he recovered from that to net his first international goals in a year.
There were a couple of defensive errors this evening, with Johan Djourou and Phil Jones among those responsible. However, probably the worst of the lot came from Steve von Bergen, who fired a clearance straight to Sterling in the first half. England couldn't make the most of it as the Liverpool teenager's pass to Rooney was poor, but it gifted the visitors their first opening of the encounter and helped them to grow in confidence.
Cuneyt Cakir had a decent game this evening, dishing out just two yellow cards. He dealt with two rash challenges from Fabian Delph well early on, while he also got an early call against Jones spot on. There was a penalty shout for England in the second half as Delph was brought down by Djourou, but once again the Turkish official made the right decision in waving the claims away.
Switzerland: Switzerland will be expected to pick up their first points of the campaign when they take on Slovenia next month.
England: Things get easier for England too as they host minnows San Marino at Wembley on October 10.