Barca had started the day top of La Liga yet found itself back in third position by the time its game kicked-off after earlier victories for Real Madrid and Atletico Madrid had moved the capital sides above their Catalan rivals.
Lionel Messi soon eased any home-crowd worries that the Barca would finish the day anywhere other than back on top spot with an early headed goal.
Suarez doubled Barca's advantage just beyond the hour mark before grabbing two more from the penalty spot.
A third penalty was dispatched by Neymar on 85 minutes after Ognjen Vranjes was shown a second yellow card for nudging the Brazilian in the box, to the dismay of Sporting's players.
Suarez then rounded off the scoring as the final whistle approached, striking the ball beyond Ivan Cuellar in the Sporting goal after being played through by Messi.
The Uruguayan's goal haul was all the more remarkable given he had put four past Deportivo La Coruna in his side's 8-0 romp over the Galicians on Wednesday -- a match which ended a three match losing streak for the reigning Spanish and European champion.
Barca heads the La Liga standings with three games remaining despite being level on points with second placed Atletico.
Luis Enrique's side has a better head-to-head record against Atletico this season as well as a far superior goal difference thanks in part to the lethal form of Messi, Neymar and Suarez.
Atletico had earlier defeated Malaga 1-0 at home through a deflected Angel Correa strike.
However, Atletico's delight in victory was spoiled somewhat as manager, Diego Simeone, was sent to the stand after a bizarre incident that saw an extra ball thrown from the direction of the Atletico bench when Malaga burst forward on a promising break at 0-0.
Although it didn't appear to be Simeone who threw the ball, it was he the referee sent to the stand for the indiscretion.
Despite angry protestations from fans and the Atletico bench, Simeone later told reporters that the referee had made the "correct decision," in comments carried by the AFP news agency.
Atletico will fear the inspirational Argentine coach could now also face a touchline ban.
Real Madrid remains a point behind Barca and Atletico after it battled back from two goals down to defeat crosstown rival, Rayo Vallecano.
Gareth Bale grabbed a brace either side of a Lucas Vazquez strike to ensure Zinedine Zidane's side, which was missing Cristiano Ronaldo, remains in the title hunt.
PSG completes part two of treble
Paris Saint Germain beat Lille 2-1 to win the French League Cup final and complete the second leg of a potential treble.
Angel Di Maria scored the winning goal for the Parisians after Djibril Sidibe had canceled out Javier Pastore's opener.
PSG has already been crowned league champions after dominating Ligue 1 this season.
It will look to complete a domestic clean sweep of trophies when it faces off against Marseille in the French Cup final on May 21.