Alphonso Davies scored Canada's first-ever World Cup goal with a towering header on Sunday, in just the second minute.

But the 2018 runners-up responded with two goals from Kramaric, plus strikes from Marko Livaja and Lovro Majer.

Croatia and Morocco, who caused another upset by beating Belgium 2-0 earlier Sunday, both have four points from two matches. Belgium have three points but still have a chance to advance.

Canada are out, though, despite an energetic performance from John Herdman's team and a blistering start.

The outstanding Davies, of Bayern Munich, headed a cross from Tajon Buchanan just out of goalkeeper Dominik Livakovic's reach inside 70 seconds, to the delight of their red-shirted Canadian fans.

"I am disappointed in the result. It was not easy," said Davies, who had a penalty saved in the opening loss to Belgium.

"We did our best, we fought the entire game. We're looking forward to the next game and hopefully we get some points."

Kramaric looked to have scored for Croatia in the 26th minute but he was ruled offside. However, his second chance counted 10 minutes later when he made it 1-1 with a precise left-foot shot.

Livaja put Croatia in front with a low shot from outside the penalty area in the 44th minute. Kramaric added his second in the 70th minute with another neat finish from Ivan Perisic's cross.

Canada were well beaten by the time Majer scored in stoppage time after a horrible mistake by defender Kamal Miller.

When Miller failed to control the ball on halfway, Mislav Orsic broke clear and unselfishly squared for Majer to clip the ball into the roof of the net.

"We made a small step here but we are far from our ultimate goal," said Croatia coach Zlatko Dalic. "Croatia demonstrated power, strength and quality and nobody is happier than me about that.

"We played an extraordinary Canada, they were full of energy. They scored a goal in the first minutes that gave them more energy and power, but we managed to stabilise ourselves."

Croatia's hackles were up going into the match after Canada coach John Herdman had said his side were going to "eff" them, a pithy comment that undoubtedly supplied the script for his counterpart Zlatko Dalic's team talk.

Yet Canada flew out of the blocks with the fastest goal of the tournament so far, when Davies headed home.

"It was a great start and a proud moment, especially for the fans in the stadium and the people back home. We got to celebrate something that we have been waiting a long time for," Herdman said.

In the end though, youthful energy and attacking intent was no match for the experience and know-how of the Croatians and goalkeeper Milan Borjan was forced to work hard to keep the score down.

Canada was also eliminated in the group stage of the team's only other World Cup appearance in 1986 and their trip to soccer's biggest tournament will end on Thursday against Morocco.

Croatia now need just a point from their final group game, against Belgium, to guarantee qualifying for the knockout stage.

with agencies

Australian Associated Press