Despite scoring the only goal of the first half through Neal McAuley, the Saffrons trailed 0-13 to 1-7 at the break.
Ciaran Clarke stole the show by scoring Antrim's entire second-half tally of a goal and eight to secure the draw.
Armagh also drew in 2A, ending 1-13 apiece at home to London.
It took a late goal by Caily Gorman and equalising point by Eoin McGuinness to deny London victory at the Athletic Grounds.
Antrim will be satisfied with taking something from their trip to Carlow who had started the division with victory over Westmeath.
They wanted to build on the opening win over London as they aim to enjoy a better year after a disappointing 2016 campaign.
Carlow finished with 13 men after Richard Coady was shown a straight red and Dion Wall picked up a second yellow.
In Saturday's Division 3B fixture, former Antrim player Liam Watson scored 2-10 as Warwickshire beat Fermanagh 2-12 to 0-9 at Brewster Park.
Antrim came away from Cullen Park with a hard-earned point as they drew 2-15 to 0-21 against Carlow in Division 2A of the Hurling League.