Ivan Rakitic pounced to open the scoring from close-range midway through the first half before Suarez added to the Catalan's advantage just after half-time.
Fran Rico pulled one back for Granada from the penalty spot but Lionel Messi restored Barcelona's two-goal advantage 20 minutes from the end when set up by Suarez.
After losing at home to Malaga last weekend, Luis Enrique's men were keen to ensure they fell no further behind arch rivals Real Madrid in the La Liga standings.
The result means Barca moves to within one point of Real who play Villarreal Sunday.
"I am very happy and satisfied with the work the players did in very special conditions," Enrique told reporters after the match.
"The teams have to be commended for the game they played on grass like that. They both tried to play a passing game, and that's worth highlighting."
Enrique had rotated his squad after midweek victory at Manchester City in the Champions League.
Barcelona legend Xavi returned to the starting lineup but the potent attacking triumvirate of Messi, Suarez and Neymar remained in place.
The purposeful, all-action performance of Suarez, who scored twice in midweek against City, came in for particular praise from Enrique.
"Ever since he arrived, Suárez has been playing top class football and working very hard," he said.
"He may look more spectacular now and people are seeing more of him, but he has always been a special player that does a lot for the team."
United triumph after red card botch
With Chelsea and Tottenham contesting the League Cup final at Wembley Sunday, there was a reduced fixture card in England Saturday.
Wayne Rooney scored two second half goals as Manchester United overcame ten-man Sunderland at Old Trafford to keep up its chase for a Champions League spot.
But United old-boy Wes Brown was sent off under controversial circumstances after it appeared referee Roger East mistook him for team-mate John O'Shea who looked to have fouled Red Devils' striker Radamel Falcao.
Although Sunderland players complained that Brown had not touched Falcao, East stood by his decision after consulting with his assistants.
Elsewhere, relegation threatened Burnley fell 1-0 at home to Swansea City while Stoke City overcame Hull City by the same scoreline at the Britannia Stadium.
Newcastle United ensured Tim Sherwood's tricky start to life as Aston Villa manager continued with Papiss Cisse scoring as the only goal as the Magpies won 1-0 at St. James' Park.
An early goal from West Brom's young striker Saido Berahino, meanwhile, was enough to ease out Southampton at the Hawthorns.
In the Premier Leagues early fixture Crystal Palace upset West Ham 3-1. Striker Glen Murray scored twice for Palace before being sent off for a second bookable offense late on.
Dortmund revival continues
Borussia Dortmund's Bundesliga resurrection continued with a 3-0 home victory over local rivals Schalke in the Ruhr derby.
Although the scoreline and performance were ultimately convincing, Dortmund didn't break the deadlock until Pierre-Emerick Aubameyang scored in the 78th minute.
Henrikh Mkhitaryan added a second four minutes from the end before Marco Reus rounded off the scoring in injury time.
The win is Dortmund's fourth in a row in the league and pushes Jurgen Klopp's men further clear of the relegation zone they occupied only a matter of weeks ago.