The Croatians qualified directly for this stage having finished second in their domestic league last season, while Guimaraes defeated Puskas Academy in the previous round.
Match preview
Indeed, Hajduk Split's second-placed position represented the club's best league finish since the 2011-12 season.
Croatia has effectively been a one team league for several years now, with Dinamo Zagreb winning 16 of the last 17 top tier titles.
As such, most sides are often playing for second spot, making Hajduk Split's achievement last season impressive, even if it is a slightly depressing reality for a club which reached the quarter-finals of the Champions League as recently as 1995.
Head coach Valdas Dambrauskas is the man tasked with taking the Masters from the Sea beyond the qualifying stages of European competition for the first time since the 2010-11 Europa League campaign, with Guimaraes representing a tricky obstacle to overcome.
After all, Guimaraes are considerably more used to competing in big European games in recent times, having reached the group stage of the Europa League three times in the past nine seasons.
Since being promoted in the 2006-07 season, they have consistently punched above their weight, never finishing below 10th place in Portugal's top league.
However, The Conquerors have lost their top goalscorer from the past two seasons after Oscar Estupinan departed for Championship side Hull City, with head coach Pepa following his star striker out of the door after receiving a big-money offer from Saudi Arabian side Al-Tai.
The Portuguese side, who finished sixth in the Primeira Liga last season, dealt with these setbacks impressively to dispatch Hungarian side Puskas Academy 3-0 across two legs, but they will undoubtedly face a much bigger test when they travel to Croatia on Thursday.
Hajduk Split form (all competitions):
Vitoria de Guimaraes Europa Conference League form:
Team News
Hajduk Split do not appear to have any injury concerns facing them ahead of Thursday's match.
As such, Dambrauskas is likely to go with the same XI which earned his side an impressive 2-0 win away to NK Istra 1961 at the weekend.
Guimaraes, meanwhile, are unlikely to have Tomas Handel available to them as the midfielder is suffering with a muscle strain.
It would be a surprise if any changes are made from the starting line-up which got the job professionally done in Hungary last Thursday.
Hajduk Split possible starting lineup:
Kalinic; Mikanovic, Borevkovic, Simic, Melnjak; Grgic, Vukovic; Mlakar, Krovinovic, Biuk; Livaja
Vitoria de Guimaraes possible starting lineup:
Varela; Maga, Amaro, Mumin, Ogawa; Semedo, Tiago Silva, Dani Silva; Lameiras, Andre Silva, Jota Silva
We say: Hajduk Split 1-0 Vitoria de Guimaraes
We believe Hajduk Split can use the visitors' lack of organisation on and off the pitch to their advantage by securing a crucial first-leg advantag.
Whether it will prove to be enough to see them progress to the next round is another matter, but it would give them something to protect in Portugal next week.