Chigumbura hit seven lusty sixes along with a boundary to give his team something to fight for with his 26-ball knock.
Left-arm spinner Axar Patel (1/18 in 4 overs) and fast bowler Jasprit Bumrah (2/24) put the brakes on the host nation. However, the trio of T20 debutants Rishi Dhawan (1/42 in 4 overs), Yuzvendra Chahal (1/38 in 4 overs) and Jaydev Unadkat (0/43 in 4 overs) gave away 123 runs in 12 overs.
Leg-spinner Chahal got a bit of stick during his final over, so did left-arm slow medium pacer Unadkat.
Hamilton Masakadza (25, 15 balls), for one, smashed three sixes -- one off seamer Dhawan and two off medium fast bowler Unadkat to get the team off the blocks quickly.
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Masakadza along with Chamu Chibhabha (20, 19 balls) added 33 runs for the opening stand in only 4.2 overs before Bumrah removed him. Masakadza tried to play a lap-scoop off a slower delivery only to be caught by Mahendra Singh Dhoni behind the stumps.
Himachal Pradesh's Rishi, who got a second chance after a disastrous tour of Australia, was hit for six boundaries and a six in his four overs. But his consolation was Chibhabha's wicket.
Sikander Raza (20, 18 balls) and Malcolm Waller (30 off 21 balls) added 47 runs for the third wicket but Chahal then bowled a googly to breach through Waller's defence.
The 97 for 3 soon became 98 for 4 after Raza was run-out after a mix-up with Chris Mutombodzi.