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Middlesex 88 for 2 (Stoneman 41) trail Durham 350 (Trevaskis 80*, Eckersley 58, Roland-Jones 4-72) by 262 runs
The 23-year-old all-rounder, who posted his first-class best of 88 at Hove last month, was left stranded on 80 after running out of partners as Durham were dismissed for exactly 350.
Heavy rain in the morning delayed the resumption of play until 2.40pm, when Tim Murtagh (three for 43) swiftly made inroads by taking wickets in successive overs.
Ned Eckersley could only add a single to his overnight 57 before being caught behind off Murtagh’s outswinger, while Ben Raine departed without scoring as a leading edge sailed tamely into the hands of mid-on.
However, Trevaskis advanced to his half-century with a confident cover drive for four off Roland-Jones and Carse (28) batted pugnaciously alongside him as the pair put on 58 for the eighth wicket.
Carse made a late, successful bid to secure a third batting bonus point, hammering Luke Hollman for successive sixes and lifting Durham above 300 with just a ball to spare before the cut-off point.
But he eventually perished to an acrobatic leg-side catch by Simpson, who reacted smartly to leap to his left and pouch Carse’s miscued hook one-handed at full stretch.
The keeper went on to collect two further catches, both off Roland-Jones, who polished off the visitors’ tail on the stroke of tea.
Chris Rushworth almost struck an early blow when Middlesex replied, finding the edge of Sam Robson’s bat with the fifth ball of the innings, but Durham skipper Scott Borthwick juggled and spilled the chance at second slip.
Robson capitalised on that let-off, finding the leg-side boundary with some regularity as he and Stoneman (41) added 86 before the left-hander – having just hit Stokes twice to the short boundary – slashed to first slip.
Nightwatchman Ethan Bamber lasted just two balls before Rushworth nipped one back to hit his stumps, with bad light halting play at the end of the over.