The hosts survived a few defensive scares to emerge with all three points and their best ever start to a domestic season, but a late Messi injury was cause for concern
A whirlwind five-minute spell in the first half saw Adriano and David Villa hit the back of the net, either side of a Bermejo goal for the visitors on the break.
Jordi Alba scored a controversial third in the second half from an offside position, but the Blaugrana's joy turned to worry late on as Messi was forced off the pitch with a suspected knee complaint.
Nevertheless, Barca recorded another three points to maintain their lead at the top of the table, with nearest challengers Atletico Madrid in action at Valencia later in the day.
With Carles Puyol and Gerard Pique remaining sidelined, Sergio Busquets was called upon once again to fill in at the back for the Blaugrana, while Villa made his third consecutive start on his road back from injury.
Barcelona began relentlessly. Messi teed up Iniesta for a shot that flashed just over, and he himself was thrice thwarted, as a pair of attempted lobs over Javi Varas failed to find the target, before the Celta keeper stood tall to deny the Argentine from close range.
It was only a matter of time before the pressure would tell, and when a scintillating passing sequence freed Pedro to race clear down the right and drill dangerously across the face of goal, Adriano’s straightforward tap in was inevitable with 21 minutes gone.
Celta, though, were not without a threat of their own. Iago Aspas had earlier exposed the hosts’ defense when he broke clear to force the best out of Victor Valdes, and when a similar run from Alex Lopez was thwarted by Valdez again, this time, Bermejo was there to slot home the rebound, only three minutes after the visitors had gone behind.
But as fast as Celta responded with the equaliser, Barcelona were even quicker to surge back in front. A fantastic backheel from Villa released Iniesta towards the byline, who did equally well to return the ball to the Spain forward for the simplest of tap-ins in the 26th minute.
Messi nearly added a third when he sprung the offside trap to face a one-on-one with Varas, but the Argentine tried too hard to round the keeper and instead lost the ball when the rest of Celta’s defence had caught up.
There were more defensive woes for Tito Villanova minutes before halftime though, as Adriano trudged off with a suspected groin injury, forcing Dani Alves to come on in his stead.
Within seconds of the restart, Aspas came close again, flashing a shot inches wide of the far post after breaching the Barca backline once more.
The Blaugrana were lacking the cutthroat intensity of the first half, but managed to find themselves a third goal, though it came in controversial circumstances. Villa’s heel flick found Alba at least a yard offside, but no call was forthcoming, and the fullback rounded Varas to slot home just past the hour mark.
The injustice seemed to deflate what was left of Celta’s spirit, as their ability on the break, so threatening in the first half, slowly tailed off as the math entered the closing stages.
There was tension around Camp Nou late on though, as Messi went down clutching his knee, eventually walking off the pitch to sit out the rest of the game after a few minutes of treatment.
Barcelona played out the remainder of the match in control to record yet another three points, but they will no doubt hope that the win did not come at a cost, as they wait to hear news on the condition of their Argentine superstar.