Gorka Pintado scored twice to get Paulo Sousa's reign as Swansea's new manager off to a winning start.
The Spanish striker pounced on a loose pass 12 minutes after the break and lifted it over Nikolay Mihaylov.
Nikita Rukavytsya got Steve McClaren's side level when three Swans defenders missed Dario Vujicevec's cross.
Casey Thomas put the Swans 2-1 up with a free header 12 minutes from time before being upended in the box at the end which Pintado converted.
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Sousa pleased with friendly win
Swansea manager Paulo Sousa:
"I am delighted with the win.
"It's important to win against a team looking for Champions League qualification, with great players and with two weeks more preparation than us.
"We made a good job of it."
Swansea: De Vries (Cornell 75); Collins (Richards 76), Monk (Serran 45), Williams, Tate (Bessone 84), Dyer (Bond 84), Pratley (Evans 87), Britton (Allen 67), Orlandi (Thomas 76), Bauza (MacDonald 46), Dobbie (Pintado 46).
Goals: Pintado 57, 90 (pen), Thomas 78.
FC Twente: Boschker (Mihaylov 46), Kuiper (Heubach 46), Wisgerhof, Brama (Akram 46), Stam (Bannink 46 (Rukavytsya 54)), N'Kufo (De Jong 63), Perez (Tiote 46), Stoch (Chery 61), Douglas, Janssen, Vujicevec. Subs not used: Hengelman.
Goals: Rukavytsya 61.
Att: 7,304
Ref: Huw Jones
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