With 12 needed off the last over number ten Bilawal Bhatti hit a six and four besides taking a double to help Pakistan overhaul a stiff 176-run target in 19.4 overs.
Opener Mukhtar Ahmed hit his second consecutive fifty during his 40-ball 62.
Zimbabwe were lifted to 175-3 by Sean Williams who hit a rapid 32-ball 58 not out with seven boundaries and a six and opener Vusi Sibanda made 46-ball 49 after winning the toss.
The series marks the return of international cricket in Pakistan since terrorist attacks on the Sri Lankan team bus in Lahore in 2009.
Pakistan won the first Twenty20 by five wickets.
The Twenty20s will be followed by three one-day internationals on May 26, 29 and 31.