Having hit an unbeaten 43 with the bat, Sabbir then took 3-11 with his leg-spin to give the hosts a 2-0 lead in the four-match series.
After skipper Mashrafe Mortaza won the toss and elected to bat, Tamim Iqbal and Soumya Sarkar made an impressive start with an opening stand of 45 in the powerplay.
Iqbal fell for 23, but Sarkar hit three sixes in his 33-ball 43.
He and Sabbir, who also cleared the rope three times, shared a stand of 30 for the second wicket before Mushfiqur Rahman and Shakib Al Hasan made useful late contributions to guide the Tigers to 167 for three.
Vusi Sibanda and Hamilton Masakadza shared a fifty stand for Zimbabwe’s first wicket, but once they fell in quick succession only Malcolm Waller, with 29, reached double figures as the tourists stumbled to 125 for eight.