Off-spinner Shoaib Bashir took a Test-best 6-81 as Zimbabwe, following on, were dismissed for 255 on the third day of four in what was the African nation's first Test in England in 22 years.
Bashir's second five-wicket haul at Trent Bridge, following his 5-70 against the West Indies last year, gave him match figures of 9-143.
Sean Williams (88) and Ben Curran fell to Bashir either side of lunch with Sikandar Raza's breezy 60 merely delaying England's win.
England laid the platform for victory in their opening match of their 2025 home season with a commanding first-innings total of 565-6 declared, that saw their top three of Zak Crawley (124), Ben Duckett (140) and Ollie Pope all score hundreds.
Although opener Brian Bennett struck Zimbabwe's fastest Test hundred, off 97 balls, in reply the tourists were still dismissed for 265, with England captain Ben Stokes taking two wickets in his first match in any kind of cricket this year.
Bashir, whose two first-class wickets this season had cost an average of 152 apiece, put some indifferent county form behind him with 3-62 in the first innings.
Stokes's side next face India in a five-match series starting in June.
Zimbabwe return to the Test arena with a two-match series at home to neighbours South Africa in June and July.
Zimbabwe revival shortlived
Williams was on course to regain the record for the fastest Test century by a Zimbabwe batsman that he had lost to opener Brian Bennett earlier in this match when, 12 minutes before lunch, he was lbw sweeping at off-spinner Shoaib Bashir for an 88 made off just 82 balls including 16 fours.
Together with obdurate opener Ben Curran, he had shared a century stand that revived Zimbabwe, following on, from the depths of 7-2 in this four-day match - the African nation's first Test in England in 22 years.
At lunch, Zimbabwe were 141-3 in their second innings - still 159 runs behind England's imposing first-innings 565-6 declared that featured hundreds from the top three of Zak Crawley (124), Ben Duckett (140) and Ollie Pope (171).
Curran - dropped twice by England captain Ben Stokes and reprieved by a review when given out lbw on the field to Bashir - was 36 not out off 96 balls, with just one four, as he dropped anchor.
Zimbabwe resumed on 30-2 with Curran four not out and fellow left-handed batsman Williams 22 not out after the 21-year-old Bennett, who broke Williams' record with a 97-ball century in his side's first-innings 265, had fallen for just one second time around.
England captain Ben Stokes brought himself on for Saturday's second over as the swing bowler looked to exploit the overcast conditions in Nottingham.
But his opening ball saw all-rounder Stokes, playing his first match of the year in any form of cricket following hamstring surgery, drop a sharp return catch off a firm drive from Curran, then on 10.
Stokes's fourth and fifth deliveries Saturday were both struck for four by Williams, a blazing cut followed by a thumping pull through midwicket.
Williams completed a 42-ball fifty with his 10th four - a straight-drive off injury-plagued fast bowler Josh Tongue, appearing in his first Test in two years.
England debutant paceman Sam Cook went round the wicket to the free-scoring Williams only for the batsman to strike a flowing cover-drive that sped to the rope - a shot cheered all the way to the boundary by the colourful band of Zimbabwe fans in the stands.
Curran - the son of the late Zimbabwe all-rounder Kevin and brother of England internationals Sam and Tom - was generally content to keep an end up.
But on 29, he mistimed a pull shot off a Tongue bouncer only for the diving Stokes to drop a tough chance at midwicket.
And on 30, Curran was given out lbw to Bashir, who took three wickets in Zimbabwe's first innings, before being reprieved by a review.
Technology went against Williams, however, when he too missed a sweep against Bashir, with his dismissal upheld on the umpire's call.