The first leg against AIK Solna will again be at Mourneview Park on 17 July and will be Linfield's 100th game in Europe.
There was an early warning for the Blues when Adeshina Lawal had a chance for the visitors but his effort went straight at Jonathan Tuffey.
After Andy Waterworth fired into the side netting Linfield moved a step closer to the next round by taking the lead on 17 minutes.
Waterworth picked out Aaron Burns who cut the ball back for Carvill and he made no mistake from close in to make it 1-0 on the night and 3-1 on aggregate.
The rest of the first half belonged to Linfield with chances for Ivan Sproule and Waterworth who hit the upright but they could not add to their lead.
Within minutes of the restart Torshavn had a lifeline when Lawal was brought down in the box by Tuffey, the ref awarded the penalty and booked the Linfield keeper.
Lawal picked himself up and rattled in the spot kick to grab a vital away goal.
That goal gave the visitors a lift and they almost went ahead on 63 minutes when Poulsen just failed to connect with a cross after being left free in the box.
It was a nervous last 10 minutes as the team from the Faroe Islands pushed for that second goal to force extra-time, but the Blues held out to the final whistle.