The tourists started the day in an extremely strong position, having skittled Zimbabwe for 176 and then reached stumps on 103 on day one.
Openers Imran Butt and Abid Ali (60) were well set and they each kicked on to post half-centuries, Butt coming nine runs short of a hundred.
But, after a show of resistance from the Zimbabwe attack, which included Pakistan captain Babar Azam going for a duck, it was Fawad who stole the show with an unbeaten 108.
He led Pakistan to 374-6 at the close, a lead of 198, and will Hasan Ali (21 off 18) for company at the crease as they look to further their control on day three.
Butt and Abid put on 115 for the first wicket, however, after the latter edged to first slip to give the breakthrough to Zimbabwe, the hosts continued their inroads as Donald Tiripano removed Azhar Ali (36) and then dismissed Babar first ball when the skipper pushed a full delivery to straight mid-on.
Yet by that point, Pakistan already had a 50-run lead and Fawad ensured that advantage would be added to considerably.
He reaped the rewards for a measured innings and his century was brought up with a four following a misfield at mid-off.
Mohammad Rizwan's 45 also helped Pakistan's cause, while Hasan struck two sixes and a four to accelerate things further before stumps.
Stumps in Harare!April 30, 2021
Fawad continues fine form
Three of Fawad's centuries have come since December 2020, with the left-hander making the most of the second act of his Test career having spent more than 10 years in the wilderness.
He scored 102 against New Zealand last Boxing Day and then 109 versus South Africa on home soil in January. His career-best remains his 168 against Sri Lanka back in 2009, but that total could be under threat if he maintains his composure here.
Babar tripped up by Donald
An ill-advised shot from Babar in which he was tempted in a risky drive off the bowling of Tiripano saw him go for a golden duck for the first time in his career. It is his first of any variety in Test cricket since October 2018 against Australia.