Having claimed a first-leg advantage last time out, the home side are in the driving seat to progress but their visitors are still in with a fighting chance.
Match preview
Twente showed great resolve to see off the threat of Heerenveen and secure a 2-1 victory when the teams faced off at the Abe Lenstra Stadion on Thursday.
Ron Jans's men opened the scoring through Vaclav Cerny in the 19th minute but were pegged back by Thom Haye just shy of half time after which Manfred Ugalde grabbed the winner in second-half stoppage time.
That was a fifth consecutive victory for The Tukkers off the back of maximum points from each of their final four matches of the just-concluded campaign where they finished fifth in the Eredivisie table.
More impressively on Twente's part, they have scored 17 goals and conceded just twice since playing out a thrilling 3-3 stalemate against Sparta Rotterdam in April.
Currently on a run of seven straight matches on home turf without defeat, Sunday's hosts are huge favourites to get the job done and keep their dreams of securing European football alive.
Conceding a last-gasp winner last time out has certainly dealt Heerenveen a huge blow heading into this weekend's contest but they were on the back foot for large spells of the contest prior to Ugalde's strike.
That was only a first defeat in five games for Kees van Wonderen's men who picked up eight points from their final four league outings to pip RKC Waalwijk to eighth place in the standings.
De Superfriezen must now pick themselves up with 90 minutes of football still left to play to determine the fate of their European ambitions.
Having lost just one of their last eight matches on the road, Sunday's visitors now go in search of crunch victory away from home which would see them avoid crashing out of this stage of the Eredivisie Conference League playoffs for the second successive season.
FC Twente Eredivisie form:
D
W
W
W
W
W
Heerenveen Eredivisie form:
L
W
D
D
W
L
Team News
Twente's Max Bruns remains unavailable for selection due to a long-term ankle problem and the 20-year-old will not play any part this weekend.
Manfred Ugalde has now found the back of the net in three straight matches for the home side, making the Dutchman one to keep an eye on here.
First-choice goalkeeper Andries Noppert recently made his return to action and is set to retain his place in between the sticks for Heerenveen.
Meanwhile, Sven van Beek and Joost van Aken are ruled out through achilles and knee problems respectively, while Timo Zaal misses out due to a muscle problem.
FC Twente possible starting lineup:
Unnerstall; Smal, Propper, Pleguezuelo, Brenet; Sadilek, Zerrouki, Vlap; Misidjan, Ugalde, Cerny
Heerenveen possible starting lineup:
Noppert; Kohlert, Bochniewicz, Van Ottele, Van Ewijk; Olsson, Haye, Tahiri; Sahraoui, Van Hooijdonk, Colassin