Rangers dominated for large spells but weren't able to hold onto a 2-0 lead in 90 minutes but ensured their progression with a Kemar Roofe goal in extra-time.
Sutton only had praise for Rangers.
“It’s an enormous achievement and credit to Giovanni van Bronckhorst and the Rangers players,” he said on BT Sport.
“I thought they disappointed over in Braga but to get to a major European semi-final is such a big deal for Rangers and Scottish football.
“They deserved to go through. They started so well and they needed to.
“[James] Tavernier has been prolific in Europe for them this season. [Borna] Barisic has been excellent as well coming back into the team and was decent at the weekend. He has such good delivery.
“Tavernier’s finish is a brilliant finish. The goalkeeper will be disappointed with it as Tavernier doesn’t have much to aim at but slots it perfectly.
“The roof nearly came off the stadium but they needed that fast start. They didn’t create nearly enough chances in Portugal but that fast start was absolutely key.
“I fancied Rangers to go through comfortably. It wasn’t all that comfortable in the end but they got there.
“The players would have been kicking themselves when they conceded late on. They created big opportunities and had a numerical advantage, the tie should have been over.
“Credit Rangers for digging deep again.”