The win doubled the joy for the hosts as the match brought international cricket home for the first time since attacks on the Sri Lankan team bus in Lahore in March 2009.
Strict security was in place with 4,000 policemen on duty, but that did not stop cricket-deprived fans from packing the 27,000 capacity stadium.
Pakistan opener Mukhtar Ahmed hit a maiden half century during his rapid 45-ball 83 to help Pakistan achieve their best Twenty chase in 19.3 overs and take a 1-0 lead in the two-match series.
Fans lined up for entry five hours before the start of the match at 7pm local time (1500GMT) and had to go through five check points before entering the stadium.
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Fire works opened the match with Pakistan president Mamnoon Hussain introduced to the teams.
On the field, Pakistan bettered their highest Twenty20 chase by one run, beating the 172 they chased against Bangladesh at Pallekele in 2012.
Mukhtar hit 12 fours and three sixes before he edged spinner Greame Cremer behind the wicket.
Pakistan also lost Mohammad Hafeez (12), Umar Akmal (four) and Shoaib Malik (seven) in a mini-slump before skipper Shahid Afridi hit the winning boundary in a nervy finish.
Earlier Zimbabwe got off to a flier with opener Hamilton Masakadza (43) and Vusi Sibanda (13) racing to 58 in 6.5 overs before recalled paceman Mohammad Sami dismissing both off succesive deliveries.
Sami, playing his first international match for three years, dismissed Raza to finish with 3-36.
Chigumbura ensured Zimbabwe get to a respectable total by hitting three boundaries in paceman Wahab Riaz's 18th over and then hit a six off Sami in the next to reach his second Twenty20 half century.
Chigumbura's previous best T20 score was 53 not out he made against United Arab Emirates at Sylhet in Bangladesh last year.