The recent Arsenal signing, who came in for the injured Daniel Sturridge, put the Three Lions in front just before the hour-mark and wrapped up the points in stoppage time as the Swiss poured forward.
And despite their late foray forward, the Swiss were unable to breach a stubborn England rearguard as the visitors fly home happy.
Switzerland 0-2 England
Euro 2016 qualifier
St Jakob Park, Basel
8 September 2014
Roy Hodgson made two changes to the side that started in the 1-0 win over Norway five days earlier. With the injury to Sturridge, Welbeck came in, while Fabian Delph earned a first start following an energetic debut from the bench against the last week.
There was also a change in formation as Hodgson opted for three in midfield with Raheem Sterling in behind the front two of Welbeck and captain Wayne Rooney.
England began brightly inside an electric St Jakob Park - Welbeck and Sterling's movement causing particular concern for the home side.
However, a couple of slips, first from Delph, who picked up an early booking for a second lunging tackle, then Wilshere, gave the hosts a chance to go forward. Both attacks ended in nothing.
Switzerland were caught out by Sterling on 15 minutes, and he powered forward before rolling into the path of Rooney inside the box. The Manchester United man set himself, but scuffed his side-foot effort into the hands of keeper Yann Sommer.
Rooney then connected with a delightfully driven Leighton Baines cross from the left, but it was not easy to deal with and the ball arrowed behind.
Welbeck continued to cause a nuisance too, as he poked the ball past Steve von Bergen wide on the left and drove in towards the box. But he appeared to be caught in two minds - shoot or cross to Rooney or Sterling arriving in support - and his square pass evaded both.
Switzerland had a rare sight on Joe Hart's goal soon after. A cross from the left was cleared to Stephan Lichtsteiner 20 yards out, but the Juventus defender's shot flew just over the bar.
Hart needed to be at his best seconds later when Haris Seferovic was put through with just the keeper to beat. From an angle the Eintracht Frankfurt striker drove across goal, but Hart's outstretched leg denied them the lead.
At times, England's quick, one-touch football in attacking areas left the Swiss in knots. When Delph and Baines combined on the left to play in to Rooney's feet, the skipper's sharp turn opened up the space for a shot. His curled effort was good, dipping in front of Sommer, who could only palm away for a corner.
The Borussia Monchengladbach stopper was again called to action from the corner, Phil Jones meeting the cross with a powerful downward header, but Sommer cleared well to keep it level at the break.
The second half started in similar fashion, with England creating a couple of early openings as the Swiss tried to counter. Jack Wilshere fired just wide and when Sterling and Jordan Henderson linked up around the box, the ball almost found its way in off the leg of defender Valon Behrami.
Action was end to end, and Sterling almost wriggled clear when Hart bowled magnificently into his path on the halfway line.
The Manchester City keeper then stood firm when Switzerland responded through Seferovic's sizzling volley.
And it proved to be a vital save as England soon went in front.
Sterling, again finding space on the left, drove forward and teased a perfect delivery across the face of goal. Despite Swiss legs stretching with all their might, they could not stop the ball finding Welbeck arriving at the back post to tuck away.
The strike seemed to spur the Swiss on and they enjoyed their best period, catching England out and almost levelling matters.
Josip Drmic was denied by a last-ditch slide by Gary Cahill after the substitute had gone around Hart. Then Seferovic came close again when he was picked out unmarked inside the area. His volley cannoned off the bar and away, but the linesman's flag was up anyway.
James Milner was introduced for his 50th appearance in place of Wilshere as England looked to protect their advantage, then Jones went down injured, so on came Phil Jagielka. Hodgson's side needed to calm the opposition a little as they searched for a leveller.
Despite pouring men forward, they could not add the finishing touch to their forward play and break down England's defence.
Sterling was often a release valve in wide areas and when he went forward and combined with Liverpool team-mate Rickie Lambert, the ball eventually reached Welbeck joining in the attack unmanned.
He made no mistake, slipping past Sommer for his 10th goal for his country and the Three Lions claimed an away victory that gets their campaign off to a magnificent start.
Switzerland (4-3-3): 1 Yann Sommer; 2 Stephan Lichsteiner, 20 Johann Djourou, 5 Steve von Bergen, 13 Ricardo Rodriguez; 11 Valon Behrami, 8 Gokhan Inler, 10 Granit Xhaka, 23 Xherdan Shaquiri, 9 Haris Seferovic, 18 Admir Mehmedi.
Substitutes: 19 Josip Drmic for Mehmedi 64, 15 Blerim Dzemaili for Zhaka 74.
England (4-1-2-1-2): 1 Joe Hart (Man City); 2 John Stones (Everton), 5 Gary Cahill (Chelsea), 6 Phil Jones (Man Utd), 3 Leighton Baines (Everton); 7 Jack Wilshere (Arsenal); 4 Jordan Henderson (Liverpool), 8 Fabian Delph (Aston Villa); 11 Raheem Sterling (Liverpool); 10 Wayne Rooney (Man Utd, captain), 9 Danny Welbeck (Arsenal).
Substitutes: 16 James Milner (Man City) for Wilshere 73, 14 Phil Jagielka (Everton) for Jones 76, 19 Rickie Lambert (Liverpool) for Rooney.
Subs not used: 12 Danny Rose (Tottenham), 13 Fraser Forster (Southampton), 15 Calum Chambers (Arsenal), 17 Alex Oxlade-Chamberlain (Arsenal), 18 Andros Townsend (Tottenham).
Bookings: Delph, Lambert.
Goals: Welbeck 58, 90.
Referee: Cuneyt Cakir (Turkey)
Assistant referees: Bahattin Duran & Tarik Ongun (Turkey)