The Bluebirds broke a run of three successive Championship draws and moved to within three points of the play-off places thanks to the Boro striker's moment of misfortune in the second minute.
The lacklustre defeat ended Middlesbrough's resurgent four-game unbeaten run and continued Jonathan Woodgate's difficult start to his managerial career.
Cardiff had only scored two league goals in the month of September but they got a helping hand to get them off the mark after two minutes.
Josh Murphy used his pace to win a corner which he curled towards the near post. In a desperate bid to clear the danger, Boro striker Fletcher turned towards his own goal and flashed a header past Darren Randolph and into his own net.
Fletcher attempted to make amends by nodding a loose ball past Smithies, but Sean Morrison was on hand to hook the ball away from goal.
Cardiff failed to extend their lead despite a dominant opening 45 minutes, but Bogle had a chance three minutes after the restart after being played in by Joe Ralls.
Bogle could only poke the ball wide, and Cardiff almost paid for their missed opportunity when Saville blasted the ball just over after a cushioned header from Ryan Shotton set up the chance.
Cardiff had two penalty shouts turned down within a minute after Gavin Whyte was shoved by Marvin Johnson and Callum Paterson was barged over in the box by Anfernee Dijksteel but their appeals were waved away by referee Darren Bond.
Bogle looked as if he was going to celebrate his first start in 637 days with a goal when he beat Shotton to Junior Hoilett's teasing cross, but his header crashed against the crossbar.
There was more danger for Woodgate's men when Randolph palmed Aden Flint's header back into the danger area for Paterson to head just over the bar and onto the roof of the net.
Boro made a rare foray into Cardiff territory in search of a late leveller, but in the end the own goal was the only thing that could split the teams after a game lacking attacking quality.