Replying to the home side's mammoth total of 565-6 declared, Bennett struck 139 off 143 deliveries as the African side were bowled out for 265 before going to stumps on 30-2 in their follow-on innings.
The 21-year-old opener went to his hundred off just 97 balls, beating the mark set by teammate Sean Williams, who scored a century off 106 deliveries against New Zealand in 2016.
Bennett also became Zimbabwe third Test centurion against England, joining Andy Flower and Murray Goodwin, who hit 148 not out at the same Trent Bridge venue 25 years ago.
Bennett's herculean effort, which included 26 fours, was not enough for Zimbabwe to avoid the follow-on though next top-score in the innings was only 42 that came from captain Craig Ervine.
The African country will go into the third day still trailing by 270 runs with Bennett and Ervine already back in the dressing room in the second innings with Williams (22 not out) and Ben Curran (2 not out) at the crease.
England had earlier batted for 45 minutes at the start of the second day after after a barnstorming opening day in which the hosts racked up a total of 498-3.
England top three in the batting order of Zak Crawley (124), Ben Duckett (140) and Ollie Pope (171) all scored centuries while Harry Brook added a quick-fire 58 as the home side breached the 560-run mark.
England allrounder Jamie Overton has been ruled out of the remainder of the white-ball series against West Indies after sustaining a fractured right little finger during the first ODI at Edgbaston.
Jofra Archer has been ruled out England's ODI series against West Indies, that starts later this month, due to a thumb injury sustained with IPL side Rajasthan Royals.
England head coach Brendon McCullum has confirmed that seamer Sam Cook will make his Test debut against Zimbabwe at Trent Bridge on Thursday.
Captain Ben Stokes is "very confident" he can fulfill his role as an all-rounder in England's Test team ahead of a busy home schedule as he returns from hamstring surgery.
