The Spanish Super Cup semi-final defeat to Atletico Madrid 10 days ago prompted Barca to sack Ernesto Valverde and replace him with former Real Betis coach Setien.
And the 61-year-old kicked off his reign at the Nou Camp with three points, his new side finally breaking their opponents down courtesy of Messi's 12th goal in as many games against Granada.
The visitors hit the post through Yan Brice, but could not secure their first point at this ground as they failed to hold out with 10 men after German's dismissal 21 minutes from time.
They almost went ahead in the sixth minute but Rui Silva parried out Ansu Fati's low shot.
Fati, on the stretch, then prodded an effort over the top after excellent play from Messi, who could not keep a curling 25-yard free-kick under the crossbar.
Arturo Vidal had a weak shot saved by Silva before Granada threatened for the first time just before the half-hour when Carlos Fernandez drilled an effort wide.
Messi almost gave Barca the lead on the stroke of half-time, firing a Jordi Alba cutback into the side-netting when well placed in the area.
Barcelona picked up where they left off at the start of the second half without creating any clear-cut chances, struggling to make inroads on the stubborn Granada defence as Messi and Ivan Rakitic fired shots wide.
After Alvaro Vadillo blazed a free-kick hopelessly over, Granada offered a warning sign to Barca in a rare attack in the 65th minute.
Brice beat Marc-Andre Ter Stegen and saw his low 20-yard effort cannon back off the inside of the post.
Granada were soon on the back foot though as, after Antoine Griezmann had a shot saved, they were reduced to 10 men when defender German tripped Messi and received a second yellow card.
And they paid the price with 14 minutes remaining following a fine goal from Messi.
The playmaker started the move with a pass to Griezmann on the edge of the box and, after the Frenchman's flick found Vidal, Messi converted the midfielder's backheel by rolling the ball into the corner of the net.
Barca refused to settle for one goal as Messi had a shot parried wide by Silva and Griezmann fired into the side-netting from a tight angle.