Fiji captain Alivereti Doviverata admitted his side took time to warm up before they eased to victory over Japan in Townsville.
The South Sea islanders outscored Japan five-tries-to one in a stop-start display marred by poor handling from both sides.
But after reaching the break 16-13 up, Fiji powered clear to win 41-13 and keep alive their hopes of a first quarter-final berth since 1987.
First, they face a potential Pool B runners-up decider against Scotland on 1 November, assuming France stay undefeated.
"We had our game plan set out before but it was a bit tense out there in the first 20 minutes," said Doviverata, whose wife gave birth to their first child - a girl - in a Suva hospital during the match.
"But as the game went on we got the ball rolling and did what we wanted to do.
"It was an important game for us - a do-or-die match - but the boys will be happy and will have a rest before starting again next week for the game against Scotland."
The flanker insisted that Japan had provided a stern test for Fiji and admitted they were fast improving as rugby nation.
"A lot has been said about Japanese rugby in the past but they've shown they have gone up a notch and will be a team to reckon with in the future," he said.
The Fijians now face an uphill struggle after a number of players injured themselves against Japan.
Fly-half Waisale Serevi has a suspected broken collarbone, scrum-half Sami Rabaka has a suspected broken metatarsal and flanker Alivereti Mocelutu has a broken forearm.
Fiji coach Mac McCallion said: "They will all undergo scans on Friday to ascertain whether they are as serious as is suspected.
"While I believe we have the strength in depth to cover we may need to call up one replacement. But we will sleep on it and make a decision in the morning."