There was nothing in the pitch to assist Best when Di Venuto and Benkenstein resumed on 54-3.
Hampshire earned an early breakthrough when James Tomlinson had Michael Di Venuto caught at gully by Crawley.
Anderson removed Mark Stoneman, stand-in skipper Michael Di Venuto, Collingwood and Phil Mustard.
Opener Michael Di Venuto was dropped three times and should have been run out before being dismissed for only 17.
Flintoff was again frustrated as Mohammad Yousuf just failed to grasp a difficult opportunity when Di Venuto pushed to short-leg.
But Di Venuto was relatively untroubled in going to his century off 161 balls, surviving one serious lbw appeal on 95.
Top scorer Michael Di Venuto was run out for 24 as Lancashire romped to a first Championship win of the season.
Naqaash then ended an opening stand of 48 when Durham's prolific Tasmanian Michael di Venuto edged his first ball to second slip.
BBC: SPORT | Cricket | Counties | Chanderpaul fails on home debut
The 31-year-old will join Australian Michael Di Venuto at the Counyt Ground, but will not be available until June because of international commitments.
Benkenstein completed his half-century off 108 balls with 10 fours soon after lunch, before Di Venuto cruised to a century which included 14 fours.
But Mustard hit three fours in the second over and di Venuto saw them home with 14 fours and a six in his 91.
BBC: SPORT | Cricket | Counties | Durham claim remarkable victory
Michael Di Venuto also hit a century against his former county.
"The thought of he and Michael Di Venuto batting together will give a lot of opposition bowlers a real headache, " said Derbyshire captain Dominic Cork.
Mark Chilton's direct hit from cover then ran out Di Venuto after Mustard sent him back, before Mustard edged Anderson high to Law at second slip.
Hampshire's sizeable task took on herculean proportions as Gibson found the edge of Michael Lumb and Ervine's bat and Di Venuto held on at second slip.
With the target down to 36 off 13 overs, West Indian Shivnarine Chanderpaul helped di Venuto to tick off the remaining runs with an assured 16 not out.
BBC: SPORT | Cricket | Counties | Durham claim remarkable victory
Derbyshire made light of the early loss of Australian Michael Di Venuto as Matthew Dowman (65) and Matthew Cassar (43) shared a century stand for the second wicket.
Denly followed leg before to a ball that kept low one run later and when Matthew Walker cut Wiseman to Michael di Venuto at slip, Kent were 80-3.
BBC: SPORT | Cricket | Counties | Durham remain in title contention
Pace soon gave way to spin as the light deteriorated, Adil Rashid being driven for four in his first over to bring Di Venuto his fifty from 82 balls.
Following Benkenstein's dismissal, Ian Blackwell and Di Venuto steered Durham to their first bonus point of the match before rain stopped play with 51 overs of the day remaining.
Phil Mustard was strong on both sides of the wicket and motored on despite the departure of Michael Di Venuto, who was brilliantly caught by Michael Carberry at mid-wicket.
Last man Simon Kerrigan fell caught behind to Mitch Claydon one ball after Sutton reached three figures, leaving Durham openers Stoneman and Michael di Venuto 13 overs to negotiate before the close.
Pietersen survived the hat-trick ball but edged just beyond Di Venuto off Neil Killeen before inevitably falling to that man Gibson, who pinned him in front of off-stump with one he angled in.
Yorkshire overseas signing Tino Best was once again wicketless, though the West Indies fast bowler may have been unfortunate when Di Venuto shouldered arms to a delivery which swung back in to him on 95.
Ten more runs were ticked off before Michael Di Venuto took a smart catch to dismiss David Balcombe off Davies, but Imran Tahir joined Ervine to add the 21 runs required and ease Hampshire's relegation worries.
And it could have been worse had Michael di Venuto (31 not out) not survived a controversial incident when on six, Michael Lumb claiming a low catch at first slip off Dimitri Mascarenhas, only for the batsman to stand his ground and be given not out.
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