Wales face the Pacific Islanders on Thursday after their bruising 28-25 win over the hosts at Twickenham.
England then face Australia two days later.
“If we beat Fiji we’ll put quite a bit of pressure on England I suppose because they’ll have to beat Australia,” said Gatland, who has three fresh injury worries.
Centre Scott Williams hurt a knee and wing Hallam Amos suffered a shoulder and seem set to miss the rest of the tournament.
Full-back Liam Williams was concussed after a blow to the head in the same passage of play and is unlikely to face Fiji.
Wales trailed 25-18 to England at the time but, with three backs playing out of position, they rallied to claim a crucial victory.
On Sunday Australia beat uruguay 65-3 to join Wales on nine points at the top of the table.
Fiji have lost their opening two games – 35-11 to England and 28-13 against Australia – but New Zealander Gatland believes they have been unlucky.
“It’s massive for us,” he said.
“We’ve spoken that if we could win today and win against Fiji then that game England v Australia becomes huge and the pool could be over by that stage.
“I think they’ve been pretty unlucky and we have to make sure we respect them.
“But I think we can take a lot of confidence out of this performance.”
Gatland says a lot of effort has been put in to preparing for the short turnaround between these two matches.
“This isn’t anything new to us. We’ve gone through meticulously various scenarios… to make sure we prepare the players the best we can,” he added.