Although Vladimir Petkovic's side have already guaranteed a play-off spot via the Nations League the win means they are just a point behind Group D leaders Republic and Denmark with two matches remaining in their campaign.
They also have the better of the head-to-head record with the Irish as the two teams drew 1-1 in September.
Mick McCarthy's outfit's destiny will come down to their final game of the campaign against Denmark, a match they need to win to qualify.
Captain Duffy and right-back Seamus Coleman will both miss the fixture in Dublin after picking up yellow and red cards respectively.
McCarthy, in his second spell as Republic coach, made three changes from Saturday's draw at Georgia which included handing 19-year-old striker Aaron Connolly his first international start.
Petkovic kept faith in the starting lineup which lost 1-0 to Denmark at the weekend.
The hosts claimed an early lead as Benfica's Seferovic scored his first international goal since November after a quarter of an hour.
McCarthy's side's could have equalised with four minutes of the first half to play but Shane Duffy fired his header straight to Yann Sommer.
Defender Ricardo Rodriguez missed a chance to make sure of all three points but his 77th minute penalty was saved superbly by Darren Randolph.
Everton right-back Seamus Coleman was shown a red card for a hand ball which resulted in the spot kick.
The home side's second goal came as Duffy deflected Edimilson Fernandes' injury time effort into an empty net.
Switzerland host Georgia on November 15 and travel to Gibraltar three days later, the same day the Republic welcome Denmark.
Standout matches today