The Cook Islands were made to work for the win by Wales in their opening game of the World Cup, with Tony Iro’s side running out 18-12 victors in Leigh.
In the other Group D game, Tonga edged past Papua New Guinea 24-18 in St Helens on Tuesday evening.
The Cook Islands face Tonga and Papua New Guinea in their remaining group games, with it looking like they need one more win to progress to the knockout stages. Wales, meanwhile, would have to beat Tonga and Papua New Guinea to qualify for the knockouts.
Wales started in fine form, with the Swinton captain Rhodri Lloyd opening the scoring. Matty Fozard, now at Widnes, converted to give Wales an early 6-0 lead.
The Cook Islands levelled the score midway through the first half through former Wigan centre Anthony Gelling, with Steven Marsters converting.
Bridgend-born Ollie Olds, now playing for Valley Diehards in Australia, put Wales back in front on the half hour mark.
Kukis winger Steve Marsters added a penalty goal just before the half-time hooter to reduce the half-time deficit at 12-8.
HT: Wales 12-8 Cook Islands
Tony Iro’s Cook Islands came back into the game in the second half. Their forwards gained big metres through the middle of the park.
The Kukis took the lead for the first time in the game on the hour mark. South Sydney Rabbitohs youngster Davvy Moale crashed over.
And the Cook Islands were in again just moments later when Steven Marsters collected a chip into the corner to produce an excellent finish. He couldn’t convert but they led 18-12 with 15 minutes to go.
Wales had a great chance to level things up at the death through Caleb Aekins, but the Kukis managed to keep them out to hold on for an 18-12 win.
Wales: Aekins; Butt, W Evans, Kear, Williams; O Olds, Ralph; Walker, Fozard, Fleming, Lloyd, Antrobus, Burke. Subs: Butler, B Evans, Curtis Davies, Connor Davies. 18th man: Tom Hopkins.
Tries: Lloyd, O Olds Goals: Fozard 2
Cook Islands: Iro; S Marsters, Gelling, R Rennie, Ulberg; E Marsters, Ford; Petterson-Robati, Teroi, Moeroa, Peyroux, Porter, Tetevano. Subs: Makatoa, Moale, Ngatikaura, Takairangi. 18th man: Noovao-McGreal.
Tries: Gelling, Moale, S Marsters Goals: Marsters 3