Luke Norris gave the hosts an 11th minute lead as he rose above Conor McLaughlin to nod home Darnell Furlong’s cross at the back stick.
But Fleetwood fought back as Ash Hunter put the ball on a plate for David Ball to sweep home his ninth of the season from close range in the 22nd minute.
Swindon were awarded a penalty by referee Darren Deadman in the 49th minute after skipper Nathan Pond was ruled to have impeded Jermaine Hylton but Cairns was on hand to tip away Michael Doughty’s spot-kick.
And Rosler hailed Cairns.
He said: “Fantastic
“That was a match-winning performance today from Alex.
“He was good and he normally does well as he is an outfield player with gloves on, that is what I always call him.
“And today he made crucial saves especially the penalty.”
Rosler says he was happy with the point which saw Fleetwood drop to eighth in the League One table after Southend’s 2-0 win at Oldham.
But say: “I’m happy with the point.
“To be brutally honest I think in the first half we were the better team.
“We gave a very cheap goal away first time the ball came into the box.
“Second half they been the better team on the ball.
“We had still the penalty situation.
I think when the referee gives the one against Pondy he has to give the one for Devante.
“We hit the bar and we had a shot saved on the line.”