Mbappe netted either side of the storm which delayed the second half to move alongside Miroslav Klose on 16 World Cup goals, behind only Lionel Messi who took the record to 18 with two goals against Austria earlier on Monday (Tuesday AEST).
"I think it's the first time I experienced it in football as a coach or a player," Iraq's Australian boss Graham Arnold said of the delay.
"It obviously made it much harder for the players."
Mbappe might have made a dream start with less than two minutes on the clock had Manu Kone's cross from the right found the Real Madrid star at the far post.
An Ousmane Dembele effort was gathered under pressure by Iraqi keeper Ahmed Basil in the 13th minute, before Mbappe broke the deadlock.
After being played in by Olise, his 20-yard drive brushed the fingertips of Basil before finding the back of the net.
France were in cruise control and it was only their seeming desire to set up Mbappe at every opportunity that denied them the chance to extend their lead.
Iraq had their hopes of clawing back into the match take a hit when Aymen Hussein, goalscorer in their opening 4-1 defeat to Norway, was forced off due to injury.
His replacement, Ali Al Hamadi, fired wide but France remained unruffled as the humid atmosphere was punctured by a dramatic rainstorm shortly before halftime.
The whistle sent both sides scurrying for cover with FIFA announcing that the match had entered "severe weather mode" due to the possibility of lightning strikes.
"It's a question of safety," Les Bleus coach Didier Deschamps said.
"You can't fight against rain and lightning. We will stick to the local laws. We have to adapt. These are very special circumstances and I do hope they will not happen again."
After a delay of two hours 11 minutes from the halftime whistle, the players returned with France continuing to dominate.
Mbappe was gifted his second goal – and fourth of the tournament – as Iraqi goalkeeper Ahmed Basil was unable to control an overhit pass from Ahmed Qasem, the ball running loose to Dembele who squared for Mbappe to stroke the ball home.
Dembele then fired wide, but finally claimed his first World Cup goal seconds later, steering the ball past Basil after being found by Olise's through ball.
Iraq went close to pulling a goal back when Al Hamadi was unable to stretch far enough to turn the ball in at the far post.
Mbappe created one final chance for himself before being replaced in the 90th minute, picking the ball up near halfway before outpacing the defence, only to fire high and wide.
"He (Mbappe) can take (Lionel) Messi, he can take (Cristiano) Ronaldo," Deschamps added.
"He does have the capacity to up his ante."
With the AP.
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