Groenewald plundered four for 41 as the visitors skittled out their hosts for 114 in just 35.2 overs in their second innings at Trent Bridge to win by 133 runs.
Somerset’s charge came after they themselves had been dismissed for just 161 inside 44 overs with Vernon Philander claiming three for 47 on a day when a total of 22 wickets fell.
All-rounder Keith Barker, whose unbeaten 102 was the major contribution in Warwickshire’s first innings total of 450 all out, helped to reduce Durham to 189 for four in their second stint at the crease with a three-wicket blitz to add to the four he claimed first time around.
The visitors, who had resumed at 50 for three, could manage only 185 in their first innings with Paul Collingwood’s 68 not out the only significant score as they were forced to follow on 265 runs behind.
Opener Mark Stoneman survived a torrid start to the second innings to finish day three unbeaten on 83, but Keaton Jennings, Scott Borthwick and Michael Richardson all fell to Barker to finish in 189 for four, still 76 runs behind and with a fight on their hands to avoid defeat.
Division One leaders Middlesex look to be heading for stalemate against Hampshire after former England opener Nick Compton scored his first century for the county since rejoining from Somerset.
Compton’s knock helped the visitors to 362 in reply to Hampshire’s first innings total of 413, and with the home side finishing day three on four without loss, the prospects of anything other than a draw seem remote at best.
In Division Two, leaders Lancashire will head into the final day of their showdown with Leicestershire at Grace Road leading by 158 runs and with eight wickets intact after building on a first innings lead of 119.
They finished a rain-affected day, on which Kyle Jarvis had earlier taken five for 69, on 39 for two to leave themselves in a strong position.
Ryan ten Doeschate led an Essex fightback after Glamorgan had threatened to take control by reducing the visitors to 86 for three.
His 38 not out helped to steady the ship as they finished day two on 183 for four in reply to Glamorgan’s 314 all out, in which Craig Meschede scored 68 off just 52 balls.
There was a maiden half-century for Calum Haggett as Kent edged to a slim first innings lead over Gloucestershire at Bristol.
Haggett made 54 as he and Matt Coles put on 119 for the eighth wicket as the visitors recovered from 98 for seven to finish a rain-truncated day on 223 for nine, a lead of 30, with Liam Norwell and David Payne taking three wickets each.
Hail ended proceedings prematurely at Wantage Road with the weather allowing only two hours’ play on day two during which Northamptonshire’s Stephen Peters collected his fourth championship half-century of the season.
He finished the day on 64 not out from a total of 107 for two with Surrey having managed to bowl a total of just 28 overs in the game to date.