Lionel Messi overcame a tardy start to score twice in the second half to give the Catalan giants a comfortable lead heading into the return leg at Camp Nou in three weeks' time.
Arsene Wenger will come away from this game frustrated as his game plan worked well for over an hour before Luis Enrique's Barca hit the home side on the break in rapid style in the 71st minute.
It took 16 seconds to fly down the other end after Gerrard Pique had cleared in defence with Luis Suarez playing in Neymar who cut back for an unmarked Messi to take a first touch, sitting Petr Cech down, before firing home his 440th goal for the club.
12 minutes later and the Argentine maestro had doubled his team's advantage when beating Cech for a second time - the only two goals he has scored against him in his career - from the penalty spot.
Messi arrived at Per Mertesacker's poor clearance before Arsenal substitute Mathieu Flamini who cut down the star left-footer, leaving referee Cuneyt Cakir with absolutely no doubt, and allowing the Barcelona man to send Cech the wrong.
Earlier in proceedings, Arsenal had created some top chances but were inefficient in the final third which has been their downfall in recent times.
Alex Oxlade-Chamberlain had a fantastic opportunity to give the Gunners the lead in the 22nd minute but his effort from close range, after Hector Bellerin's initial attempt had been blocked, was struck straight at Marc-Andre ter Stegen.
On the stroke of half-time, Suarez found himself with space at the back post but placed his header across the face of goal in what was Barcelona's first real chance of the contest.
Cech was called on to deny Messi early in the second half before ter Stegen did well to keep out Olivier Giroud's header, beating a looming Aaron Ramsey to the ball.
In the 67th minute, Mertesacker threw his body on the line to produce a top quality block to thwart Messi before Giroud made a very odd choice down the other end when in a great goalscoring position, opting to pick out a pass towards the byline for Theo Walcott, who had in fact ran the other way.
Arsenal had been enjoying their best spell in the game when Barcelona struck and it all happened so quickly, breaking the hearts of the Gunners who would have been daring to dream to just moments earlier.
In the end, the class of the reigning European champions shone through and they will take a nice advantage into the return bout in Spain on March 16.
2015/16 UEFA Champions League - Round of 16 first leg