The Blaugrana secured a crucial win at Camp Nou to temporarily close the gap on Real Madrid atop the Liga table while Javier Clemente's side remain in a relegation battle
Andres Iniesta gave Barca the lead in the dying minutes of the first half before the dramatic spell after the break that saw Pique controversially dismissed. David Barral then turned home the equaliser with a deft touch at the near post, but Pep Guardiola's side never shied away from the challenge in front of them as strikes from Keita and Xavi ensured a 12th home win of the season.
Barcelona struggled for much of the first half as they were unable to penetrate a resolute Sporting defence, but they looked promising in the early exchanges as they dominated both territory and possession.
The Blaugrana continued to probe and came close when Adriano embarked on a burst forward, beating four Sporting defenders in the process. The Brazilian worked a sight of goal but he directed his shot wide of the far post as they came closer to taking the lead.
Sporting's solid defensive work was finally undone three minutes prior to the break. Adriano and Keita combined brilliantly, allowing the former to roll the ball across the six-yard box and into the path of Iniesta who had the simplest of tasks to notch his first La Liga goal of the season.
Cesc Fabregas came close to doubling Barca's lead minutes later when he burst onto Dani Alves' through ball. He flicked a shot towards goal but Juan Pablo was there to deny the former Arsenal man with a reactionary stop ensuring his side remained in touch with the Blaugrana at the break.
In a dramatic start to the second half Pique was shown a red card after the referee adjudged the Catalan defender to have denied Miguel de las Cuevas a clear, goalscoring opportunity.
Clemente responded by introducing topscorer Barral and his gamble was immediately repaid. After directing the resulting free-kick against the wall with his first touch, Barral's second found the back of the net when he turned home Formose Mendy's low cross.
Despite the numerical advantage bestowed upon them, Los Rojiblancos returned to their defensive duties as Barcelona looked to re-establish their lead. Iniesta replicated Lionel Messi with a superb run from deep as he turned Sporting's Galvez with a wonderful touch. He then burst forward, bearing down on the opposition defence only for his pass to be too heavy for Alexis Sanchez.
The winner came in phenomenal fashion when Keita curled home a lofted drive from 20 yards with a magnificent finish. Alexis linked the play up brilliantly before the Mali international showed his class with an unstoppable effort.
Xavi then secured all three points for the home side when he latched onto Iniesta's chipped pass and clipped the ball neatly over Juan Pablo.
Barcelona, now provisionally seven points behind Real Madrid at the top of La Liga, return to Champions League duty on Wednesday as they look to secure a spot in the next round at the expense of German side Leverkusen, with Pep Guardiola's side taking a 3-1 lead into the second leg at Camp Nou.
Madrid host Espanyol at the Santiago Bernabeu in La Liga on Sunday.