Pay-per-play signing Kieron Dyer stabbed home his first league goal in six years for an early opener and Sammy Ameobi, who arrived on loan from Newcastle, cracked in a sizzling second soon after to put Boro in control of a dominant first half.
But Cardiff hit back after the break and pulled one back through Aron Gunnarsson before creating chances to level in a frantic finale.
"The character got us through," said Mowbray, whose side had taken just four points from nine games and slipped out of the play-off places in a torrid start to 2013.
"Sometimes when you have been on a run like we have you forget how to win football matches.
"It has been a tough run and sometimes we haven't got what we deserved but we worked and we battled and showed real character and we got through in the end.
"Cardiff gave us a lot of problems in the second half. They had some big lads in our box and at times it was like Land of the Giants. It was frantic at the end but we got there."