Having watched Manchester City usurp them at the summit with a 3-2 win in the early kick-off at Swansea City, Arsene Wenger's side looked set to lose their grip on first place as managerless Cardiff frustrated them for long periods.
Watched by prospective new boss Ole Gunnar Solskjaer - who flanked controversial owner Vincent Tan in the Emirates Stadium directors' box - Cardiff held out until Bendtner slammed home in the 89th minute.
Theo Walcott added gloss to the scoreline with a chipped finish in stoppage time to hand Wenger’s side a one-point advantage at the top.
Lukas Podolski made his second league start of the season, leading the line for an Arsenal side lacking Olivier Giroud (ankle), Aaron Ramsey (thigh), Mesut Ozil (shoulder) and Kieran Gibbs (calf), although Jack Wilshere and Walcott came through late checks on respective ankle and shoulder problems.
Cardiff forward Craig Bellamy missed out due to his chronic knee problem, while experienced right-back Kevin McNaughton made a first Premier League appearance.
Wilshere and Walcott combined in the 13th minute as the latter prodded a searching cross into the side netting after a lacklustre opening.
England midfielder Wilshere was the standout performer in the opening half hour and was unfortunate not to win a penalty when he was bundled over by Gary Medel.
Arsenal goalkeeper Wojciech Szczesny made the game's first save of note as Jordon Mutch stormed forward on the counter-attack, before Santi Cazorla beat McNaughton and teed up Walcott to ripple the side netting once more in the 31st minute.
Podolski's unease in the lone-striker role was underlined in first-half stoppage time, as the Germany international was crowded out when well placed in the Cardiff box.
Wenger's men began the second half with greater intent and former Tottenham centre-back Steven Caulker made a fine last-ditch challenge to thwart Podolski, but it was then Cardiff's turn to have a penalty appeal waved away by referee Jon Moss when Craig Noone's cross struck Nacho Monreal's arm.
Goalkeeper David Marshall was booked for time wasting as Arsenal laid siege to the Cardiff goal and he was grateful to see the ball go behind off his near post after Wilshere had bustled in from the left to blast goalwards in the 64th minute.
Per Mertesacker then hit the same upright as he spurned a second free header in a matter of minutes.
Bendtner, on for the ineffective Podolski, failed to make headed contact with the goal gaping as a frustrating afternoon appeared to be slipping away from Arsenal, but he was on hand to convert after had Marshall saved well from Bacary Sagna's header.
Walcott then completed the win by lifting the ball over Marshall in stoppage time, leaving Cardiff a point above the relegation zone and Solskjaer with much to ponder.
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