The champion needed three points to reclaim top spot in LaLiga from Real Madrid but were mostly blunted by a disciplined defensive display in windy conditions in Catalonia.
Setien set his side up in a 3-4-3 variation reminiscent of Pep Guardiola's old formation but, despite enjoying close to 82 per cent of the possession, clear-cut chances were hard to come by.
Barca was given an advantage when German Sanchez was sent off and Messi eventually made the breakthrough with 14 minutes of normal time left as the attack finally clicked into gear.
Setien's much-discussed adherence to the Johan Cruyff school was clear in a first half in which Barcelona made more than 500 passes, but a shot from Messi that rippled the side-netting was the closest they came to a goal.
Messi saw a free-kick deflected over the crossbar before Granada gave Barca a real scare, Yan Eteki's low strike beating Marc-Andre ter Stegen only to bounce back off the inside of the post and away to safety.
Granada's game plan was working well until German was shown a second yellow card 69 minutes in for a trip on Messi, before Setien earned a cheer from the home fans by introducing Riqui Puig for Ivan Rakitic.
The 20-year-old made a telling impact, winning back possession on the edge of the box before Messi found Antoine Griezmann, he flicked the ball to Arturo Vidal and the Chilean's backheel was swept home by the captain.