The two teams were already guaranteed qualification to the competition's knock-off stages, and after the big win, Barcelona are now group C winners with 13 points, followed by Sporting in second with nine.
Thierry Henry (14), Gerard Pique (17), Lionel Messi (50), Marco Caneira (own goal) and Bojan Krkic scored the visitors' five goals, While Miguel Veloso (65) and Derlei (66) scored Sporting's consolation.
After 14 minutes, Barcelona started showing full control of the game with an early lead. Lionel Messi was allowed to storm his way in the Sporting box, the Argentine dished out an assist to Henry who easily tapped in from close range.
Three minutes later, Barcelona added a second when a high ball was ricocheted off Anderson Polga and Gerard Pique and ended in the back of the net.
After the interval, Josip Guradiola's men were able to find the net once again thanks to a Messi shot from the edge of the box.
The home side finally got back in the game with a double-minute salvo from Miguel Veloso and substitute striker Derlei.
Veloso curled in a powerful left-footed free kick from 30 yards out that left Oscar Valdes helpless in the Barcelona goal.
One minute later, Marco Caneira was forced to score an own goal against the home side.
On 73 minutes, substitute Bojan Krkic won Barcelona a penalty after a reckless tackle from Rui Patricio, which saw the keeper sent off. The young striker stepped up to successfully convert from the spot and score his team's fifth goal of the night.
In the Group's other game, Shakhtar Donetsk earned themselves a UEFA Cup spot, after thrashing visitors FC Basel 5-0.
Brazilian midfielder Jadson was man of the match as he scored a hat-trick against the Swiss outfit (32, 65, 73). Fellow Brazilian full-back Willian and Yevhen Seleznyov scored Shakhtar's other two goals.
Shakhtar are still third of the group with six points, while Basel remain rooted to the bottom with one draw and four defeats in the competition so far.