The Gunners, who were knocked off the summit of the Premier League table after Manchester City's victory in the early kick-off at Swansea, were frustrated by some stubborn defending in wet and windy conditions in North London for 87 minutes.
However, the much-maligned Bendtner rifled into the roof of the net after David Marshall had made a fine save to block Bacary Sagna's header to break the deadlock.
In injury-time, a deft touch from Jack Wilshere pierced the Cardiff backline and Walcott dinked home for his fifth goal in as many matches to seal the points.
The Welsh side were well organised by caretaker boss David Kerslake and were seemingly eager to impress the watching Ole Gunnar Solskjaer who is poised to become the club's new manager.
PICTURED: Ole Gunnar Solskjaer and Cardiff owner Vincent Tan watch on at the Emirates pic.twitter.com/GMzeEVikRt— MailOnline Sport (@MailSport) January 1, 2014
Arsenal did have strong claims for a first-half penalty when Gary Medel appeared to hook the leg of Wilshere in the box.
Before that, Wilshere, operating in an advanced central role in the absence of the injured Mesut Ozil and Aaron Ramsey, had teed up Walcott and Santi Cazorla although both failed to find the target.
Walcott put further efforts over the top after cutting in from the right and into the side netting with his less-favoured left foot after Cazorla tricked his way to the by-line.
Arsenal's first half was summed up when Lukas Podolski, leading the line in the absence of the injured Oliver Giroud, failed to get a shot off when he found himself with his back to the goal six yards out.
Indeed, the only time a keeper was called into action in the opening 45 was when Jordon Mutch ran at Laurent Koscielny on the counter-attack and forced Wojciech Szczesny to save with his legs.
0 - Each of Arsenal's last four Premier League games have been 0-0 at half-time. Snooze.— OptaJoe (@OptaJoe) January 1, 2014
Cardiff had penalty claims of their own shortly after the break when Nacho Monreal handled Craig Noone's cross, but their appeals were waved away.
Marshall was booked for time wasting with over 30 minutes to go, and that was a sign of Cardiff's intentions as they defended deep and in numbers.
Wilshere struck a shot with venom against the post before Arsene Wenger made an attacking move by bringing on Bendtner and Tomas Rosicky for Podolski and Mathieu Flamini.
Per Mertesacker soon spurned the best chance of the match when presented with a free header eight yards out from Walcott's cross, but the German defender nodded wide.
A minute later, Mertesacker climbed highest once more, but his header glanced the outside of the post.
The attendance at Emirates Stadium is 60,004 this afternoon (49) 0-0 #AFCvCCFC— Arsenal FC (@Arsenal) January 1, 2014
Pressure continued to mount, and Wilshere dragged an effort from edge of the box wide and Walcott put a free-kick onto the roof of the net.
It looked like it was not to be Arsenal's day when Walcott's lovely cross from the right evaded Bendtner's head, but the late goals see them restore their one-point advantage over City at the top of the table.
Although the opening goal came at a cost with Bendtner coming off with an injury after scoring the goal and it looks likely to rule him out for some time.
Cardiff caretaker manager Kerslake was disappointed that his side did not hold out, telling the BBC:
It's hugely disappointing. The players have given their all and I thought they had done enough to get a draw. We knew we would be good enough to soak the pressure, not a lot of teams can do that.
|Wojciech Szczesny||B||David Marshall||B|
|Bacary Sagna||B||Kevin McNaughton||B|
|Per Mertesacker||B||Ben Turner||B+|
|Laurent Koscielny||B+||Steven Caulker||A-|
|Nacho Monreal||B+||Declan John||B|
|Mathieu Flamini||B-||Gary Medel||C|
|Mikel Arteta||B-||Craig Noone||C|
|Jack Wilshere||A-||Bo-Kyung Kim||C|
|Theo Walcott||B+||Jordon Mutch||B-|
|Santi Cazorla||B||Peter Whittingham||C-|
|Lukas Podolski||C-||Fraizer Campbell||C-|
|Nicklas Bendtner||B+||Aron Gunnarsson||C|
|Tomas Rosicky||B||Don Cowie||C|
|Thomas Vermaelen||C||Nicky Maynard||C|
Arsenal face arch-rivals Tottenham in the third round of the FA Cup on Saturday and are not back in Premier League action until January 13 when they travel to Aston Villa in a Monday night game.
Cardiff face West Ham two days earlier but first travel to Newcastle on Saturday in an all-Premier League Cup tie with every chance they will have a new manager in place.