Zimbabwe started their reply brightly, but some excellent spin bowling from Mohammad Hafeez (three for 30) and Zulfiqar Babar (two for 21) put the hosts behind the required rate and they never recovered, ending their 20 overs on 160 for six.
"The players have shown great commitment and confidence," skipper Hafeez told a TV interview at the presentation.
"They are showing great trust in each other and this is something we are trying to develop in our team. We thought 150 to 160 would be good on this track but Ahmed played very well."
Zimbabwe won the toss and elected to field, but they were guilty of bowling on both sides of the wicket.
After the loss of Nasir Jamshed (23), Hafeez joined Shehzad at the crease and the pair bludgeoned their way to a second wicket partnership of 143 in under 15 overs. It was the joint-fifth highest partnership for all wickets in Twenty20 international history.
Shehzad had the opportunity to reach his century but could not get the three runs he needed off the final ball of the innings. It is still his highest Twenty20 international score. Hafeez finished not out on 54 from 40 balls.
Zimbabwe brought up their 50 in quick time before losing their first wicket, but were strangled by some excellent slow bowling.
Hamilton Masakadza (41 from 32 balls) was their best batsman, while Elton Chigumburu (35 from 19 balls) played a cameo at the end when the game was already lost.
"They got 20 too much, their two batters made it very difficult for us, but I also thought our bowlers missed their mark too many times," Zimbabwe captain Brendan Taylor said.
"They just outplayed us again and showed why they are a world-class team."
(Reporting by Nick Said in Cape Town, editing by Stephen Wood)
