Breen finished the day 12.6 seconds behind Lappi, after Friday’s final stage into Newtownards.
Dubliner Robert Barrable is in third place, one minute and 40.2 seconds off the leader.
Eight stages remain on Saturday.
Breen managed the third fastest time, just 3.1 seconds behind Lappi, in the first stage.
It was Lappi who set the pace again on stage two extending his lead to 5.2 seconds, but this time Breen responded by posting second fastest time just 2.8 seconds in arrears.
The Hamilton’s Folly stage was up next and it didn’t disappoint, Lappi again taking the stage win and Breen pushing so hard he broke the rear screen on landing over one of the Folly’s famous jumps.
But he was still only 1.9 seconds behind his Peugeot Rally Academy team-mate Kevin Abbring.
It was Lappi, Breen and Abbring that eased away from the rest of the crews over the next two stages, but Craig, though nursing some damage, checked into the mid-day service third overall.
In stage four Craig’s car landed heavy over a jump and the rear stepped out. He was lucky to escape with only a damaged rear light and bumper .
The jumps of Hamilton’s Folly accounted for Abbring challenge on the second run though, his 208 T16 damaging its radiator, causing him to retire from the rally and leading to Breen being promoted to second.
Thereafter, Breen managed to claw back vital seconds before the overnight halt.
Overall after SS10 - Newtownards TT (1.44 miles)
1 Esapekka Lappi/Janne Ferm 59mins11.2secs
2 Craig Breen/Scott Martin 0:59:23.8 (+0:12.6secs)
3 Robert Barrable/Stuart Loudon 1:00:51.4 (+1:40.2)
4 Sepp Wiegand/Frank Christian 1:01:00.2 (+1:49.0)
5 Sam Moffett/James O'Reilly 1:01:16.7 (+2:05.5)
6 Robert Consani/Maxime Vilmot 1:02:16.6 (+3:05.4)
7 Neil Simpson/Claire Mole 1:03:04.4 (+3:53.2)
8 Daniel McKenna/Arthur Kierans 1:04:56.7 (+5:45.5)
9 Josh Moffett/John Rowan 1:05:11.4 (+6:00.2)
10 Chris Ingram/Gabin Moreau 1:06:01.7 (+6:50.5)