Latvala had taken first place back from Lappi during Saturday morning with a string of stage wins and then pulled out an 8.5-second advantage.
He started the second run of the famous Ouninpohja stage at a similar pace, but after passing the first split fastest his Toyota Yaris suddenly slowed with a mechanical problem.
Though Latvala briefly got going again, he soon had to park once more and was pushed off the stage by spectators.
Tanak explains cause of Rally Spain puncture
Latvala and co-driver Miikka Anttila worked on the car in an escape road and may yet be able to rejoin but they have lost over 12 minutes.
Lappi came through fastest and now leads Rally Finland by 54s in only his fourth appearance in the World Rally Championship's top class.
"Not good. I didn't want to be leading like this," said Lappi. "It's such a shame. This is not nice."
Toyota still holds a one-two, with Juho Hanninen able to rebuild a 4.3s gap over M-Sport's rookie Teemu Suninen - who is only in his second event in a World Rally Car - in their fight for what is now second.
Tanak extends Rally GB lead, Ogier in second
Citroen chasing Ogier, Lappi, Breen line-up
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