Lionel Messi's second-half strike means that he has now scored against every team in the Spanish top flight this season, and also extended his incredible goalscoring streak to 19 consecutive games.
Celta certainly proved to be no pushovers, however, and even took a lead in the 38th minute through a close range Naxto Insa strike that reflected its encouraging first half play.
But Barca responded just before the interval, as Messi set up Tello for a splendidly taken equalizer, before converting the 21-year old forward's feed in the 73rd minute to seemingly put the visitors on their way to all three points.
However, with one minute remaining, Borja Oubina rose highest to head home the tying goal to deny the Blaugrana victory, though they still hold a 14 point lead at the top of the table.
With PSG on the horizon, interim coach Jordi Roura rang the changes, as Marc Bartra, Martin Montoya, Alex Song and Tello were all handed starts for the Catalans.
Barca, as usual had plenty of possession, but was perhaps lacking a bit of cutting edge in the final third as it struggled to create much more than half chances against a stubborn Celta defense.
The home crowd, already rocking long before kickoff, were left howling in disbelief when Park Chu-Young was bundled over by Bartra inside the area, only for the referee to wave play on.
But their side would grow in confidence as the first half wore on, and Jose Pinto had to be at his absolute best to parry a terrible deflection off Gerard Pique, before recovering in time to deny Fernandez from the rebound.
Barca had a penalty shout of their own denied when Messi went down under pressure from Vladim Demidov, but the best openings continued to fall the way of the hosts, with Borja Oubina coming close with a header from a corner.
And with seven minutes to go until halftime, Celta would get the goal that its play just about warranted. Fabian Orellana’s jerky run fooled the entire Barca defense, and despite his shot lacking any kind of power, Naxto was there to prod home from in close.
But the Catalans would hit back before the break. Messi forced Javi Varas into a sprawling save from a 25-yard free-kick, before clipping a great ball over the defense to find Tello, who opened up his body to bend a sumptuous finish into the far corner.
Neither team really shone above the other in the initial stages of the second half, though Park had a decent opportunity when he stabbed Fernandez’ cross the wrong side of the post.
But as time wore on, Celta began to abandon its attacking intent, and focus on protecting the scoreline. And that approach gave Barcelona all the momentum it needed, introducing David Villa and Andres Iniesta to provide a boost off the bench.
But it was a familiar combination that would send the Catalans into the lead, when Messi spread to Tello out wide, continued his run into the box, and stroked the return pass home from close range with 17 minutes remaining.
It seemed like the Catalans did enough to secure the win, but with stoppage time looming, Oubina headed home a cross at the far post to send the crowd into delirium and give the hosts a crucial point in their battle for survival.