Patel (3/17) and Harbhajan (2/29) ripped through the Zimbabwe batting order as the home side ended at 124/7 while chasing a target of 179 on a slow track at Harare Sports Club to give India a 1-0 lead in the two-match T20I series.
The 21-year-old left-arm spinner Patel, one of the five Indians who made T20 International debut today, and veteran off-spinner Harbhajan virtually ended the match midway into Zimbabwe run chase with quick strikes that left the home side in total disarray.
Chasing the stiff target, Zimbabwe struggled for runs with the Indians bowling a tight line and length with pacer Bhuvneshwar Kumar opening the bowling in impressive manner by giving just four runs in his first spell of two overs.
After showing some promise, the Zimbabweans just fizzled out as they failed to negotiate the guiles of Patel and Harbhajan.
Next over, Patel dismissed two Zimbabwe batsmen in the space of five balls to send the home side run chase into disarray. While Hamilton Masakadza (28) was caught at short fine leg by Kedar Jadhav, captain Elton Chigumbura (1) was clean-bowled off a gem of delivery from Patel.
Harbhajan returned to dismiss another Zimbabwe batsman -- Charles Coventry (10) -- in the 11th over to virtually end Zimbabwe's run chase. By then, the home side had been reduced to 68/4 with the asking rate soaring above 14 an over.