Victories for Real Madrid and Atletico Madrid earlier on Saturday had left Barca third by kick-off.
Lionel Messi’s looping header into an empty net gave Barca the lead.
Suarez made it 2-0 before Barca won three late penalties, the Uruguayan scoring two and Neymar the other, and Suarez converted Messi’s pass late on.
Sporting had Ognjen Vranjes harshly sent off for conceding the third penalty for a foul on Neymar.
Striker Suarez also scored four in Wednesday’s 8-0 win over Deportivo La