Despite being handicapped by a knee injury suffered in the Sunday League the previous day, Moxon hit an unbeaten 65 from 101 balls with 13 fours, taking his match aggregate to 268.
He was, at times, clearly in discomfort, but he laced his innings with some superb driving and, with David Byas, soon calmed any Yorkshire anxiety about a victory target of 123 at the start of play.
Byas was equally aggressive and robust, finishing on 58 not out from 102 balls, with 10 boundaries. The only scare came in the first over when Byas, still on nought, survived a chance to the wicketkeeper Steve Marsh when he edged Tim Wren.
But Wren and Martin McCague failed to break through and, from then on, the batsmen picked off the bowling, with Moxon again showing outstanding batsmanship. Yorkshire's progress was so swift that they secured victory 15 minutes before lunch.
Middlesex gained their fourth Championship win of the season when they beat Glamorgan by eight wickets at Colwyn Bay.
Glamorgan took their overnight total of 258 for 5 to 332 all out in almost two hours of batting, the main resistance coming from Tony Cottey and Steve Watkin. Cottey made 36 before giving a catch to slip off the bowling of Dion Nash, although he looked long and hard at the fielder, John Emburey, before walking.
Watkin made a brave fight with a straight six off Emburey and five other boundaries in a solid 30 from 40 balls before holing out to Mark Ramprakash at long-on.
Middlesex, needing 79 to win, began badly after lunch, with Paul Weekes bowled by Watkin before he had scored. There was encouragement, however, when Jason Pooley was missed by Matthew Maynard at slip off Robert Croft when on 24 as he and Ramprakash started to push the score on.
The fifty came up in the 14th over, but eight runs later Ramprakash was bowled by Neil Kendrick. John Carr then joined Pooley and the latter reached his half-century with a boundary that took Middlesex to victory.Reuse content