Kieron Dyer, who is on a pay-as-you-play basis arrangement at the Riverside, grabbed the opener with his first league goal in six years and on-loan striker Sammy Ameobi added a second.
Aron Gunnarsson pulled a goal back for Cardiff and they created chances to level in a frantic finale but Boro held on to secure the win.
"The character got us through," said Mowbray, whose side had taken just four points from nine games and slipped out of the Championship play-off places.
"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."