The tourists had gone 11 matches without success as the touring side in the longest format, stretching back to a win at Lord's in 2018, but wrapped up a crushing victory by an innings and 116 runs at Harare Sports Club on Saturday.
Hasan took 5-36 - including his 50th Test scalp - as Zimbabwe were bowled out for only 134 in the final session. Those were his best innings figures in a Test, and the paceman finished with a match haul of 9-89.
Nauman Ali also chipped in with 2-27 as the hosts folded from 92-2, Tarisai Musakanda top-scoring with 43 at the top of the order.
Pakistan were earlier bowled out for 426, Blessing Muzarabani claiming 4-73, as they secured a huge first-innings lead of 250 runs.
Babar Azam's side had resumed on 374-6 and Fawad Alam moved from 108 to 140 before he was superbly caught behind by Regis Chakabva slashing at a delivery from Muzarabani.
Hasan also fell to Muzarabani for 30, while Donald Tiripano (3-89) and Richard Ngarava (2-104) also struck before Zimbabwe folded with the bat for a second time in a short match.
One dream Test comeback for Hasan Ali! Since his return to the Test side, the pacer has taken 21 wickets in three Tests, including 19 in the last twoMay 1, 2021
Dream return for Hasan
Hasan had been absent from the Pakistan Test team for two years before making his return in January.
The 26-year-old was named man of the match after taking 10 wickets in the second Test against South Africa and carried on where he left off in Harare.
Hasan has taken 21 wickets in three Tests in a dream comeback, reaching the landmark of 50 wickets in the longest format in only his 12th game. He was unsurprisingly rewarded for a stunning performance with another man of the match award.
Zimbabwe batting frailties exploited
Zimbabwe were always going to be up against it after they were skittled out in two sessions on day one.
They showed some resistance second time around but then lost seven wickets for 42 runs. Prince Masvaure was unable to bat due to a hand injury,