Roy Hodgson's men were worth the three points in their toughest qualifying fixture in Group E - which also contains Slovenia, Estonia, Lithuania and San Marino - and could won more comfortably had their decision making in the final third been better.
As it was, Welbeck's close-range finish just before the hour and injury-time strike proved enough to inflict defeat on Vladimir Petkovic in his first game in charge of Switzerland.
Hodgson - who led Switzerland to 1994 World Cup - asked for England to up their performance level after an underwhelming friendly win over Norway last week.
And the visitors responded by edging a tight game, although Switzerland had chances to snatch at least a point.
England's breakthrough came in the 58th minute when Welbeck capped a superb team move, and the new Arsenal striker - who came in for the injured Daniel Sturridge - added a second in stoppage time as he latched onto a Rickie Lambert pass and dispatched past Yann Sommer.
The Liverpool teenager orchestrated a four-on-two counter-attack after 15 minutes by showing the Switzerland midfield a clean pair of heels, but his pass to Wayne Rooney was mishit and the captain’s tame shot went straight at Sommer.
Jones sloppily gifted possession to Xherdan Shaqiri, whose throughball found Seferovic in the area, but the striker’s shot was well saved by the foot of Joe Hart.
Jones then came agonisingly close to making the breakthrough himself, the centre-back meeting Rooney's corner with a firm header and forcing a superb save low to his left from Sommer.
England started well after the break too, Jack Wilshere combining well with debutant Fabian Delph before dragging a left-foot shot narrowly wide of the right post.
Hart's save proved crucial soon after as Welbeck broke the deadlock.
Rooney collected the ball in the centre circle and sent Sterling free down the left, with Welbeck finishing the 19-year-old's inch-perfect delivery from just outside the six-yard box.
The forward appeared offside as he collected Shaqiri's throughball before he rounded Joe Hart and shot towards goal, but Cahill recovered to make a superb goalline block.
