Sinclair scored twice from the spot in last weekend's thrashing of Crystal Palace and the former Chelsea man took his tally to 17 goals for the season four minutes from time after he had been brought down by Barnsley goalkeeper Luke Steele.
Bobby Hassell had put the Tykes in front in the first half with his first goal in over a year, but the Swans rallied in the second half and were rewarded by Sinclair's fifth goal in his last four games.
The point was not enough to keep them in second spot, with arch-rivals Cardiff and Norwich winning to go above them, but it did at least end their run of defeats away from the Liberty Stadium.
Barnsley went into the game without a recognised central defenders, so Hassell and Nathan Doyle filled in at the heart of their defence.
But the Tykes made a bright start and Swans goalkeeper Dorus De Vries was called into action to keep out Hugo Colace's eighth-minute drive.
De Vries was unable to prevent Barnsley from going in front five minutes later though, when Hassell rose to meet Jacob Butterfield's corner with a header which crossed the line despite the best efforts of a Swans defender on the goal line.
The Swans remained on the back foot and De Vries did well to palm away Garry O'Connor's left-foot effort.
Luke Moore had a chance to open his Swansea account but Luke Steele comfortably saved his 25th-minute strike.
Swansea were starting to get into their stride and Ashley Williams was first to Mark Gower's corner but Steele palmed away the Wales defender's right-foot shot.
The visitors were finding it difficult to break down Barnsley but Williams spurned an excellent chance to equalise 62 minutes in when he headed Sinclair's cross over the bar.
Three minutes later Steele made a fine save to keep out a goalbound 30-yard free-kick from Swans midfielder Gower.
Swansea boss Rodgers made a double substitution with just over 20 minutes remaining, with Stephen Dobbie and Cedric Van der Gun entering the fray.
Midfielder Leon Britton also came on 15 minutes from time after rejoining the club from Sheffield United this week as the Welsh side pressed for an equaliser.
Highly-rated midfielder Darren Pratley picked out Sinclair but the winger headed wide from 12 yards out with 13 minutes remaining as Barnsley came under increasing pressure.
But Sinclair made amends from the spot four minutes from time when he was upended by Steele and picked himself up to slot home from 12 yards out.
And Moore could have snatched all three points a minute from time but the striker fired into the side-netting.