Barcelona dominated possession throughout, but Celta struck first after the visitors lost possession in their half, leading to midfielder Nacho Insa receiving Fabian Orellana's short pass that he poked just inside the upright in the 38th.
Messi cued up Tello to pull Barcelona level five minutes later with a lobbed pass to beat Celta's flimsy offside trap, with Tello curling the ball with a right-footed shot around the goalkeeper and off the base of the far post.
Roura sent Iniesta on and striker David Villa followed three minutes later as Barcelona sought the winner.
With Villa up front, Messi had more room to maneuver and he soon played Tello wide on the left flank before sliding forward to meet his return cross and drive it in with a low left-footed strike.
Messi has a league-leading 43 goals through 29 rounds and 56 overall this season. He has 30 goals during his unprecedented run of scoring in 19 straight rounds, shattering the previous mark of 10 straight games.
Celta, which was fighting to escape the relegation zone, made one last desperate push, and it paid off when Dani Alves failed to check Oubina at the far post to turn in Orellana's cross.
"What Leo is doing is an unheard of feat in the league's history and it shows the importance he has and his greatness as a player," said Roura. "With time, we will give him even more credit for what he's doing."
Eric Abidal, who was named to Barcelona's squad for the first time since receiving a liver transplant last year, never left the bench.
Barcelona head coach Tito Vilanova didn't travel with the team after returning this week from a 10-week medical stay in New York where he received treatment after the removal of a throat tumor in December. He may accompany the team on Tuesday.
"We're very happy to have Eric back with us," said Messi. "Tito looks very motivated, and it's important that he's with us for the final stretch of the season."