The teams meet again at Harare Sports Club on Saturday to decide who wins the first of three series, with three one-day internationals and two Tests to follow.
Afghanistan, who suffered a last-ball loss on Wednesday, won the toss and, thanks mainly to the recalled Rasooli who made 58, posted 153-6 off 20 overs.
Rasooli, one of three changes to the team, struck a six and six fours off 42 deliveries.
Azmatullah Omarzai (28) and Gulbadin Naib (26 not out) were other Afghans to make important contributions while leg-spinner Ryan Burl and seamer Trevor Gwandu took two wickets each for Zimbabwe.
In reply, Zimbabwe opener Brian Bennett struck 27, but once he departed, leaving the hosts struggling at 49 for four, only captain Sikandar Raza (35) proved a match for the Afghan attack.
Just one of the other Zimbabwe batters -- first-match hero Tashinga Musekiwa -- reached double figures as Zimbabwe were dismissed for 103 in 17.4 overs.
Naveen, who finished with 3-19, and star leg-spinner Rashid (3-20) inflicted most of the damage, ably supported by Mujeeb Ur Rahman's 2-30.
"We are still struggling to establish a strong top order, but the way Darwish played was very impressive," said Afghanistan captain Rashid.
"We are always searching for someone who bats well at four. Darwish was looking good in the nets and we were waiting for him to take that form onto the pitch.
"The way the guys bowled was very impressive after missing our lines and lengths in the first match. It was about keeping it simple and hitting the right areas."
Raza said: "Our Achilles heel was once again our batting. We are still struggling to post good totals consistently.
"Our bowling and fielding were fantastic. It was a better wicket than on Wednesday, and we were confident we could reach the 154-run target. That is why this loss hurts so much.
"Afghanistan were semi-finalists at the recent T20 World Cup. So, if you want to beat them, you have to beat them in all departments."
Brief scores
Afghanistan 153-6 in 20 overs (Darwish Rasooli 58, Azmatullah Omarzai 28, Gulbadin Naib 26 not out; Ryan Burl 2-16, Trevor Gwandu 2-29) v Zimbabwe 103 in 17.4 overs (Sikandar Raza 35, Brian Bennett 27; Naveen-ul-Haq 3-19, Rashid Khan 3-20, Mujeeb Ur Rahman 2-30)
Result: Afghanistan win by 50 runs
Series: 1-1 with one match to play
Toss: Afghanistan
