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Durham 147 (Handscomb 54, Finn 4-41) and 191 (Robson 64) beat Middlesex 143 (Raine 5-26) and 151 (Robson 65, Carse 6-26) by 44 runs
Brydon Carse produced a career-best six-wicket haul as Durham beat Middlesex by 44 runs at Lord's.
The South-African born seamer took 6 for 26 including a match-winning post-lunch burst of 5 for 9 as Durham bowled out the hosts for 151 on the third afternoon.
Victory keeps alive Durham chances of promotion, while defeat for Middlesex means they will spend a third successive season in Division 2 in 2020.
Middlesex began the day needing 175 more to win, but it didn't take long for their chase to hit a bend in the road.
Nick Gubbins hit two early fours, but his stay was an all-too brief one as he nicked the 16th ball of the day bowled by Carse into the hands of Alex Lees at slip.
Stephen Eskinazi lasted just three balls before becoming Chris Rushworth's 61st victim of the season, trapped LBW after only getting half forward.
And when the home side's skipper and batting talisman Dawid Malan followed shortly afterwards LBW to Ben Raine, they were 45 for 3.
In contrast to his playing partners, Sam Robson (65) played with increasing authority, producing trademark square cuts and some beautiful on-drives in reaching 50 off 87 balls with 10 fours, the fifth time he had passed the landmark in Championship cricket this summer.
Max Holden, despite struggling to find any touch, provided valuable support in a stand of 54 before Raine returned to pin him in front shortly before lunch.
And when Rushworth ended Robson's vigil with just the fourth ball after the resumption, the hosts were struggling again at 107-5.
Under clear skies, a sharp contrast to much of the rest of the match, batting should have been an easier proposition. But Carse struck twice in the space of three balls, first finding the edge of George Scott's bat to give Ned Eckersley another catch, before removing the normally obdurate James Harris second ball for nought.
Debutante Miguel Cummins had shown some batting promise in the first innings but he too came under Carse's spell, a Yorker ending his brief stay.
The five-for came when Simpson, Middlesex's last hope of unlikely salvation, also had his furniture disturbed.
And the wicket which sealed the career-best brought victory when last man Tim Murtagh missed with a big slog, sending his stumps awry.
Brydon Carse six-for rips through Middlesex resistance
South-African born seamer took 6 for 26 including a match-winning post-lunch burst of 5 for 9
Robson grit gives Middlesex tough task in low-scorer
Hard-fought half-century sets brother's side tricky target in fourth innings
Ben Raine hits back after Steven Finn fizzes on bowling day at Lord's
Middlesex slip to 87 for 7 after Steven Finn's four-for helps dismantle Durham