Santi Cazorla broke the deadlock for the Gunners with a fine volley in the 19th minute after his initial header had hit the post.
Aaron Ramsey then continued his superb form with a stunning strike from outside the area just before the hour mark and Liverpool could not find a response.
Arsenal, without midfielder Jack Wilshere who had been troubled by an ankle problem, created the first opening on six minutes when Tomas Rosicky was played into the right side of the penalty area and his low shot across goal was pushed behind by Simon Mignolet.
Liverpool, though, were soon on the offensive as Jordan Henderson waltzed all the way into the Arsenal penalty area, before scuffing his shot.
The visitors then settled into a good spell of possession, as Arsenal chased shadows.
Arsenal, though, swept into the lead on 19 minutes. A quick break down the right found Bacary Sagna on the overlap. His cross was behind Olivier Giroud, but fell perfectly for Cazorla on the penalty spot.
The Spaniard's bullet header beat Mignolet, but cannoned back off the post. Cazorla, though, was first to the rebound ahead of a static Martin Skrtel and lashed a fine half-volley back past the goalkeeper.
Liverpool were understandably rattled after being so dominant - and were left further aggrieved when Suarez took a quick free-kick after being pushed over by Sagna, which released Daniel Sturridge who crossed for Henderson to tap into the net - only for referee Martin Atkinson to pull play back and book the Arsenal defender.
Arsenal pressed again as Ramsey got into the left side of the penalty area and his low shot was palmed away by Mignolet at the near post.
Reds boss Brendan Rodgers made a positive change for the second half as Aly Cissokho was replaced by midfielder Phillippe Coutinho.
Suarez was released into the right side of the Arsenal box, but could only chip the ball across goal.
Liverpool broke quickly down the left through Suarez, only for his deep cross to be blasted over at the far post by Henderson.
There was a huge let-off for the visitors when a loose back-pass from former Arsenal defender Kolo Toure was seized on by Giroud, who charged into the penalty area but chipped his shot wide.
Giroud then just could not get on the end of a quick counter attack from Rosicky and Cazorla down the left.
It was, though, 2-0 on 59 minutes as Ramsey cracked home another goal of the highest order.
There seemed little danger when Mesut Ozil fed the Wales midfielder in a central position, some 20 yards out.
However, as Toure backed off, Ramsey waited for the bouncing ball to sit up before dispatching a dipping volley over Mignolet and into the back of the net.
Rodgers decided to make another attacking change as he sent on Victor Moses for Jon Flanagan.
Suarez shaved the far post from a curling effort with the outside of his right boot as the Reds looked for a way back into the match.
Mignolet saved low at his near post to deny Ozil after the German weaved into the left side of the Liverpool box.
Kieran Gibbs hobbled off after a burst down the left flank, and had to be replaced by club captain Thomas Vermaelen.
Arsenal were pressed back during the final 10 minutes, with Suarez dragging a shot wide when clean in on goal - but the hosts had already done enough to record the most impressive of their eight Premier League wins so far.