After four straight defeats, David Hodge's charges grabbed a surprise but deserved victory over the Blue Bulls to leapfrog over Midleton in the bottom two.
Carlow have four points to make up on Malone, who battled bravely but lost 33-26 to Old Crescent, to avoid being one of the two teams to drop down to the third tier for next season.
New Zealander Reuben Colquhoun grabbed Carlow's only try, with Greg Jacob chipping in with a conversion and two penalties as they got the better of promotion-chasing Barnhall.
Next time out Carlow travel to De La Salle Palmerston, who won 28-10 against UCC on Saturday to ease their own relegation worries. 'Salmo look safe now, especially with two of their last three games at home.
Elsewhere, league leaders Old Belvedere have guaranteed themselves promotion to the top flight and a home draw in the semi-finals thanks to a 10-8 win at Clonakilty.
In the sides' first ever league meeting, the Corkmen grabbed a try through Shay O'Donovan and David Lombard tagged on a penalty, but Belvo took the spoils with Rory Cushion and Eric Jackman both touching down.
Greystones, with a game in hand, strengthened their grip on second place with a 21-15 defeat of Dublin University at College Park.
'Stones kept up their excellent away record this term - they have won five games on the trot away from their Dr. Hickey Park base - with top scorer James Power converting tries from David McKechnie, Simon Malone and Dan McGettigan.
Munster's Brian O'Meara kicked three penalties, with Sean Meaney grabbing a try, as Highfield pipped Midleton 14-10 in their all-Cork clash at Woodleigh Park.
Steve Ford's Midleton side are two points adrift at the foot of the table ahead of crucial clashes with Clonakilty and Young Munster.
Fergal Campion kicked four penalties and converted Gregor Lawson's try to a 19-3 success at Thomond, which was the Dublin club's third straight win.
Suttonians' disappointing recent form continued at the JJ McDowell Memorial Grounds as Young Munster got the better of them, winning by 31-16 to move themselves up to sixth in the standings.
Derek Corcoran (3) and Mick Lynch shared out four tries for the Cookies who, with a game in hand, still have a chance of making the semi-final line-up.
DIVISION TWO: RESULTS -
Barnhall 7 County Carlow 13, Oak Park
Clonakilty 8 Old Belvedere 10, Shannonvale Cross
De La Salle Palmerston 28 UCC 10, Kilternan
Dublin University 15 Greystones 21, College Park
Highfield 14 Midleton 10, Woodleigh Park
Malone 26 Old Crescent 33, Gibson Park
Suttonians 16 Young Munster 31, JJ McDowell Park
Thomond 3 Bective Rangers 19, Liam Fitzgerald Park