Chelsea's first league win at Highbury since 1990 put the champions 20 points clear of Arsenal, all but snuffing out the title hopes of Arsene Wenger's side who suffered their third successive league defeat without scoring.
Dutchman Robben broke a bad-tempered deadlock in the 39th minute when striker Didier Drogba put him through just over the halfway line.
The speedy winger kept his head to angle a left-footed shot past Jens Lehmann from 10 metres, the ball hitting the far post before bouncing in.
It was only the second goal of the campaign for Robben who took the Premier League by storm last season but has lacked confidence recently after hamstring injury problems.
Cole made it two in the 73rd minute with another fine individual effort to win possession from Lauren on the right, cut inside and outflank England team mate Sol Campbell before poking the ball home.
"It's all good at the moment," Cole said. "We are really flying."
Arsenal also had chances in an intense but scrappy game.
Thierry Henry hit the post in the 20th minute and Dutch striker Robin van Persie had a first-half goal controversially ruled offside. Lauren, substitute Dennis Bergkamp and Robert Pires forced Petr Cech into second-half saves.
It was the Czech Rebublic goalkeeper's 50th Premier League game and his 33rd clean sheet behind a defence that has conceded only seven goals this season.
Arsenal boss Arsene Wenger bemoaned Van Persie's disallowed goal.
"It's very important to get a decision like that," he said. "In the last few games we've had decisions against us."
Wenger did not think Chelsea were the better side.
"The first goal completely changed the game," he said.
HEAD SWATHED
Seven players were booked and Chelsea midfielder Frank Lampard played much of the second half with his head swathed in bandages after a clash.
The day's ill-feeling appeared to extend to the managers.
Chelsea's Jose Mourinho disappeared down the tunnel without the customary handshake with his opposite number, continuing the pair's acrimonious relationship.
"I didn't see him," Wenger said.
Chelsea restored their nine-point lead at the top over Manchester United who won 2-0 at Aston Villa on Saturday.
In the day's other game Tottenham Hotspur earned a point in a see-saw 3-3 draw at Middlesbrough to stay in touch with the title challengers.
Tottenham went ahead in the 25th minute, Robbie Keane's shot bobbling into the net after Middlesbrough keeper Mark Schwarzer had failed to clear a high ball.
DRIFTED CLEAR
The home side's response was to attack and they were rewarded five minutes later when Aiyegbeni Yakubu drifted clear of the Spurs defence, latched on to a Gareth Southgate header and volleyed home from six metres.
Yakubu was on hand in the 43rd too when midfielder James Morrison drilled a left-footed shot from 18 metres towards the goal and it deflected into the net off the Nigerian's chest.
Spurs levelled 18 minutes into the second half when Jermaine Jenas struck an exquisite 25-metre free kick that curled over the Middlesbrough wall and past the diving Schwarzer.
Their elation was short-lived, however, as Middlesbrough defender Franck Queudrue headed a corner on to the underside of the crossbar and just over the line.
Tottenham replied in similar fashion seven minutes from time when striker Mido jumped high above the home defence to head home a Michael Carrick corner.
Tottenham remained fourth in the table, level on 30 points with Liverpool who have two games in hand after playing the club World Championship in Japan. Middlesbrough stayed 13th.
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