Hampshire began the day on 230-6 and with Callum Thorp claiming the only Hampshire wicket of the day when Wood was out lbw for 9, the visitors allowed Michael Bates to score his fifty before declaring on 275-7 at which point both sides forfeited an innings to set up a game.
With 276 from 82 overs the target, Will Smith started quickly, partnered by Michael Di Venuto, and the pair put on 23 before Di Venuto (1) was caught by Liam Dawson off Mascarenhas in the 10th over.
Mark Stoneman added 13 before he was trapped lbw by Mascarenhas as Durham reached 43-2.
The home side slumped to 54-4 when the seamer claimed his third scalp, bowling Gordon Muchall for 5, and then Will Smith was caught in the slips off Imran Tahir for 31 the following over.
Dale Benkenstein and Ian Blackwell rallied, adding 35 between them, before the latter was caught behind off Kabir Ali for 11.
A great catch from Jimmy Adams off Wood saw Benkenstein out for 26 and Callum Thorp joining Phil Mustard (28*) in the middle with Durham requiring 152 from the remaining 46 overs.
The pair gave Durham the best chance of the innings adding 64 before Thorp was caught behind off Ali on 43. Mascarenhas claimed his fourth scalp in the next over, with Claydon (2) nicking the ball to the keeper with the home side still 85 short of the target.
Mustard scored a patient fifty from 91 balls, including eight boundaries, but a misplaced cut which Michael Carberry held on to at backward point saw him dismissed on 56 with Durham requiring 60 runs from the final partnership.
It was to be Hampshire’s day and especially that of Mascarenhas who claimed the final, his sixth, wicket when Chris Rushworth (21) was caught by Ali handing the visitors a 50 run win.
Durham CCC Head Coach, Geoff Cook, said, “It’s been a frustrating week, it started last Sunday when we could have played better in testing conditions and it was disappointing to lose that game and then to have these four days following closely behind have been really frustrating with the weather. Had we played this game all the way through it would have been to our advantage and the time lost took the sting out of the game.
” It was a bit of a gamble to go for the declaration, history says that teams in that situation rarely knock off the total but on balance it was worth taking in terms of what we could have got from it.
“One or two of their guys bowled really well, the conditions were ideal for Mascarenhas and Kabir Ali, in his first game back for a while bowled very well, I thought. It was a sad game to lose but I thought the team applied themselves pretty well. Aggression and effort from the team can’t be faulted.”