The Welsh outfit have a tall order on their hands as they look to overturn a 4-1 deficit from the first leg in Slovakia last week.
Match preview
Newtown, who have never competed beyond the qualifying stages of European competition, will have little choice but to attack from the outset at Latham Park on Thursday.
After falling a goal behind via Bamidele Yusuf's close-range header in the 17th minute, Chris Hughes's side fought back after a goalkeeping blunder by Dominik Tamac allowed Henry Cowans to nick the ball off him before slotting the ball into an empty net.
However, Yusuf was a man on a mission on the day, completing a first half hat-trick. First, the Nigerian skilfully cut inside and calmly bent the ball around Newtown goalkeeper Dave Jones, before the English stopper's poor clearance allowed Yusuf to be played in behind.
Once again, the 21-year-old did not disappoint in front of goal, with his combination of pace and composure proving too much for last season's third-placed Welsh side. Alex Ivan's 75th-minute effort all but killed off the tie after the break.
Hughes will hope that an early goal can change the course of the tie in front of his side's home fans, otherwise the second leg could quickly become a non-entity.
For Spartak Trnava, who have far more pedigree in Europe having reached the semi-final of the European Cup in 1968 before progressing to the Europa League group stage as recently as the 2018-19 campaign, Thursday's trip to Wales should be little more than going through the motions.
While manager Michal Gasparik will be keen to avoid complacency within his ranks, the 40-year-old will be acutely aware that the hard work in this tie has already been done after a solid performance at Anton Malatinsky Stadium last week.
With several internationals in Spartak Tranava's squad, such as North Macedonia forward Milan Ristovski who has featured in an international tournament for his country, there is absolutely no doubt which direction this tie should go in.
However, should Gasparik find his side a goal down early on away from home, even the Slovakian cup winners could find themselves in a spot of bother if they do not keep their composure.
Newtown AFC Europa Conference League form:
Spartak Trnava Europa Conference League form:
Spartak Trnava form (all competitions):
Team News
Despite losing heavily to their opponents last week, Hughes is likely to keep faith with the same XI which he fielded in Slovakia.
That means that there will continue to be plenty of emphasis on the dynamic Cowans to support the front two from midfield in his manager's preferred 3-5-2 system.
Spartak Trnava, meanwhile, are likely to be without forward Kazeem Bolaji due to injury.
Goalscorers Yusuf and Ivan should continue to flank Ristovski in a three-pronged attack.
Newtown AFC possible starting lineup:
D Jones; Sears, Sutton, Roberts; Williams, Hughes, Cowan, Walker, M Jones; Williams, Robles
Spartak Trnava possible starting lineup:
Takac; Kostrna, Curma, Stetina, Mikovic; Savvidis, Prochazka, Stefanik; Ivan, Ristovski, Yusuf
We say: Newtown AFC 0-2 Spartak Trnava
There is a significant chasm between these two clubs and the Slovakians should have far too much for their opponents once more.
With the Welsh side having to go for it, the goal threat of Yusuf and Ivan could prove too much for them to handle with there likely to be plenty of open spaces for the duo to exploit in transition.