Andy Ryan broke the deadlock shortly before the interval in the St Patrick’s Day clash at Inver Park.
The result saw the east Antrim side move temporarily nine points clear of second-placed Cliftonville.
The north Belfast outfit suffered a shock 2-1 defeat at home against Dungannon Swifts on Saturday, with Linfield moving into second place following a 7-0 win over Newry City. David Healy’s charges are seven points behind Larne.
Speaking to the club’s media director Ian Cahoon, manager Tiernan Lynch said: “It wasn’t easy. I think we’d a much better first half than second half. We were very dominant in the first half. Second half became a little bit scrappy, but the outcome was what we wanted, a clean sheet and three points. Great credit to the boys for getting that.
"We want to make sure everyone who pays their money in, we entertain them as much as we can, but it’s very much about getting the three points at the end of it.
"It’s three points and another game chalked off. What everyone else does around us, I can’t control and I don’t get myself too involved in. I’ve to concentrate on what we’re doing. I’ve to ensure the boys are continuning to enjoy every minute of what they’re doing and they seem to be. There’s a good buzz about the place.
"This is what we’ve been trying to build for sx years. When the split comes, we wanted to find ourselves in a title race. Now we’ve got ourselves there, we’ve to enjoy it. Who knows what’s going to happen at the end of April? We just have to enjoy what we’ve left. We’ve worked really hard. We’ve to go one game at a time.”
Larne travel to Coleraine on Saturday (3pm).
Carrick Rangers suffered a 4-0 loss at home to Glentoran on Saturday.
Scoreless at the break, the visitors found the net through Niall McGinn (51 and 65), Luke McCullough (79) and Terry Devlin (88).
Speaking to Carrick’s media team, manager Stuart King said: “I thought we were really good in the first half, but we didn’t take our chances.
“Second half, once the first goal goes in, we stopped. It’s another big defeat against Glentoran. A tough day at the office. My boys gave me everything in the first half and they ran out of steam in the second half.”
Carrick travel to Seaview on Saturday (3pm) to face Crusaders.
King added: “It’s another tough one, but we’ve went away this year and won and been really dogged and ground out results. We know we’ve to do that if we’ve to get anything from Crusaders.”
Meanwhile, Ballyclare Comrades’ impressive form in the Lough 41 NIFL Championship continued as they defeated Warrenpoint Town 3-2 at Dixon Park on Saturday.
Darius Roohi opened the scoring for the Comrades on 11 minutes before Ryan Swan equalised for ‘Point on 35.
Ballyclare led 2-1 at half-time following Callum Ferris’ goal on 41.
Kealan Dillon levelled the tie on 51, but Harry Adair’s strike in stoppage time ensured all three points would be staying in south Antrim.
Ballyclare face Newington at Solitude on Saturday (3pm).