The Toyota driver, in only his fourth event at the highest level of the FIA World Rally Championship, leads his Toyota team-mate Jari-Matti Latvala and fellow young star Teemu Suninen of M-Sport in an all-Finnish top three.
After a cautious start to the rally, Lappi rose from 10th to second on the third stage of the day with the first of four consecutive stage wins that meant he went into mid-day service just 1.6 seconds behind three-time Neste Rally Finland winner Latvala.
He then continued to eat into the gap in the afternoon and grabbed the lead when he was fastest over the single run over the 21.68-kilometre Lankamaa stage. Two further stage wins increased Lappi's advantage to 4.4 seconds.
It's difficult to describe but since a small boy I've been dreaming of driving a WRC car in Finland, said Lappi. Now its happening and we're leading.
Latvala added: He's driving really, really well. All the Finns have been, it s been great. I've been doing what I can. Esapekka has been a bit quicker than me today, I'll try and improve for tomorrow.
Suninen, driving a Ford Fiesta WRC in anger for only the second time, has also starred on his home event. He added two stage wins to the one he claimed on his debut last time out in Poland, moving up to third when he went fastest on SS8 Äänekoski-Valtra. He is only 19 seconds off the lead, and he has put a 14s margin between himself and fourth-placed Craig Breen.
Juho Hänninen made it a top-four lock-out for local drivers during the afternoon in the third Toyota Yaris, but ended the day 6.1s behind Citroën driver Breen after battling suspension damage.
Mads Østberg ended the morning in third overall but he later slipped back as far as seventh with a suspected differential issue, before taking sixth back off fellow Ford driver Elfyn Evans.
Thierry Neuville was handed a great opportunity to boost his title aspirations when championship leader Sébastien Ogier crashed out on the morning's third stage, but the Belgian has struggled to show his usual pace in his Hyundai. He did gain eighth during the afternoon after Kris Meeke damaged his steering.
Ott Tänak hit trouble on the same stage as his team-mate Ogier and lost a minute and a half due to a puncture. He has moved back into the top 10 past Dani Sordo.
Jari Huttunen – like Suninen a former winner of the Future Rally Star of Finland prize drive – is in control of WRC2 on his debut in the class in a Skoda Fabia R5. He is 56.2s ahead of Quentin Gilbert.