The result left France second in the group on 10 points from four games, behind Portugal on goal difference after the European champions brushed aside Sweden 3-0. Croatia have three points and the Swedes none.
France beat Croatia 4-2 in the 2018 World Cup final before defeating them by the same score in last month’s reverse Nations League fixture.
“We knew we’d be in a real battle,” France coach Didier Deschamps told French TF1 television.
“We started very well and it’s a pity we didn’t go two goals clear as Kylian had a big chance. We did what we needed to do in the second half.
Mbappe missed a gilt-edged opportunity to make it 2-0 as he shot wide from close range with the goal at his mercy, while visiting keeper Hugo Lloris kept out Mario Pasalic’s shot from three metres with a reflex save.