Aaron Ramsey opened the scoring in the first half with a goal against his former employers. The Wales international refused to celebrate in front of his old supporters who afforded him a round of applause for the gesture.
Cardiff came out strong in the second half and looked likely to find an equaliser but substitute Mathieu Flamini rounded off a fine Gunners move late on to put the result beyond doubt.
Ramsey struck again in injury time at the end of a swift counterattack to add some extra gloss to an impressive result.
The result – Arsenal's fifth win on the road this season in the Premier League – extends the club's lead at the summit to seven points, with the rest of the top six not playing until Sunday.
Cardiff boss Malky Mackay made one change to the side that started last weekend’s 2-2 draw with Manchester United, with Kim Bo-Kyung, who scored the late equaliser against the champions, coming in for Peter Odemwingie.
Arsenal, meanwhile, made three alterations to the team that recorded a 2-0 Champions League victory over Marseille on Tuesday, bringing Kieran Gibbs, Mikel Arteta and Santi Cazorla into the starting XI in place of Nacho Monreal, Flamini and Tomas Rosicky.
The visitors were quick out of the blocks, with Jack Wilshere, who netted both of his side’s goals in midweek, rattling the crossbar inside two minutes with a left-footed curling strike from the edge of the penalty area.
A nasty clash of heads between Per Mertesacker and Bacary Sagna left the German in need of lengthy treatment in the opening stages, and Fraizer Campbell headed narrowly wide of the left-hand post for Cardiff before the defender returned to the action.
Mesut Ozil then touched the ball beyond Steven Caulker in the 15th minute to send Olivier Giroud through on goal, but the striker incorrectly assumed he was in an offside position and stopped playing. The delay gave goalkeeper David Marshall time to come off his line and block the eventual effort.
However, Ramsey broke the deadlock for Arsene Wenger’s men in the 29th minute, meeting an Ozil cross to head into the top corner for his seventh league goal of the season. Having performed Cardiff’s trademark ‘Ayatollah’ gesture before kick-off to the delight of the home fans, Ramsey refused to celebrate after putting his former employers a goal down.
Arsenal maintained their pressure after the break, with Caulker having to clear off the line from a Giroud strike following good work in the penalty area by Ramsey.
But the hosts were almost level six minutes into the second period, Wojciech Szczesny getting down brilliantly to his right to keep out a Campbell headed effort.
Kevin Theophile-Catherine drilled a long-range effort goalwards shortly afterwards as Cardiff continued to push for an equaliser, but Szczesny was equal to the strike once again.
But Arsenal doubled their advantage in the 86th minute, when Flamini smashed home from 18 yards after receiving the ball from Cazorla, before Ramsey finished off a quick Arsenal counter-attack to deliver the final blow in stoppage time.