Ilves were given a late upgrade to the UEL after the place reseved for the UECL champions was left vacant, but they were left wondering if was a punishment rather than a reward, as they were on the end of a 6-0 defeat to Shakhtar.
Played at Stadion Stozice in Ljubljana, Slovenia, Alisson put the Ukrainian side ahead midway though the first half, before turning provider for Kaua Elias who made the half-time score 2-0.
Alisson scored his second within minutes of the restart, before adding two more assists, this time for Kevin and Pedrinho. In the 89th minute, Newerton scored the sixth - the only goal the 19-year-old Alisson played no part in.
Ilves can hope for little else that restoration of pride when they host the second leg in Tampere next Thursday.
Veikkausliiga sides had no better luck in the UECL, as HJK were soundly beaten 4-0 by NSI Runavik, whose compatriots from the Faroe Islands, Klaksvik, won 2-1 away at SJK.
In the Faroes, Emil Weihe Joensen put NSI a goal up early on before Jere Kallinen received a straight red card for HJK midway through the opening half.
The home side took full advantage - Fabian Ostigard Ness added the second before the break, then two goals in seven minutes from Daniel Obbekjaer and Klaemint Olsen late on gave HJK a huge mountain to climb in next Thursday's second leg.
SJK will feel they have a much better chance of making up their deficit, but will have to do so away from home after defeat in Seinajoki.
Markus Arsalo equalised early in the second half for SJK after Jakup Andreason had put Klaksvik a goal to the good, but it was Argentinian defender Gaston Tellechea who ensured the visitors take the lead back to the Faroes, thanks to his strike in the 86th minute.
