The Swans had Andrea Orlandi in midfield in place of Leon Britton while Shefki Kuqi retained his place up front after netting the winning goal at Palace in midweek.
Newcastle recalled skipper Alan Smith to central midfield and former Cardiff loanee Wayne Routledge was out wide.
Swansea won three quick corners in the opening two minutes but play was halted as Federico Bessone suffered an injury and was replaced by Angel Rangel in the seventh minute.
The Swans were on top early on restricting the Magpies to the odd breakaways but they were unable to carve out any clear openings.
An Orlandi free-kick in the 22nd minute flew just wide as the Swans pressed home their early superiority.
The visitors' first goal attempt came on the half hour when a Fabricio Coloccini cross was headed well wide by Kevin Nolan.
The half closed with Dorus de Vries going down low to save a Nolan header from a Danny Guthrie corner.
No changes were made at the interval and Nathan Dyer had Steve Harper scrambling across goal as his cross shot flew narrowly wide.
In the 52nd minute, Darren Pratley and Dyer got in each other's way in front of goal with only Harper to beat and the chance was lost.
The Swans broke the deadlock in the 56th minute when Cotterill cut inside and beat Harper with a rasping cross-shot.
Ashley Williams headed over from close range as the Swans piled forward looking for the clinching second goal.
Newcastle came more into the game as an attacking force but the Swansea defence were superb and it was the the home side who looked more like scoring.
Substitute Gorka Pintado completely mis-kicked when in front of goal in the 82nd minute as another chance went begging.
Completely against the run of play in the 86th minute, Newcastle levelled when Carroll rose at the far post to head home a cross from Guthrie for his ninth goal of the season.
Both sides went looking for the winner but honours ended even and the point gained by the Swans moved them up to fourth, while Newcastle moved back to the top of the Championship.