Chilean midfielder Felipe Gutierrez’s 22nd-minute strike was enough to give Twente the win at the Euroborg ahead of Sunday’s return leg.
Elsewhere in the battle for Europe, fifth-placed Utrecht came out on top against their eighth-placed opponents Heerenveen thanks to a goal from Cedric van der Gun in the 69th minute.
In the race for a spot in next season’s top flight, a late goal from Xandro Schenk gave Eerste Divisie side Go Ahead Eagles the impetus ahead of their return leg against VVV Venlo, while Sparta Rotterdam hit four past Helmond Sport as they won 4-2.
Goals from Gijs Luirink, Sandro Calabro and Iliass Hassani had put the visitors 3-0 up but Helmond threatened a comeback when Davy Brouwers and Zarko Grabovac pulled two back for the home side.
However, Mimoun Mahi’s goal in the 90th minute settled a captivating game.
Promotion-hopefuls Maastricht and Volendam battled it out at De Geusselt with the visitors coming out on top thanks to a 76th-minute Brandley Kuwas goal.
Eerste Divisie side De Graafschap took on Eredivisie outfit Roda in the remaining fixture with the first leg ending up as a draw.
Anco Jansen put De Graafschap ahead on 35 minutes but the Eredivisie side drew level through Frank Demouge on 55 minutes to ensure the tie is all square ahead of Sunday’s return leg.