The match also provided useful batting practice with Ben Wright, Michael Powell and Mark Wallace scoring 50s.
Resuming on 201-6, Mark Wallace soon completed his century before he fell to Alex Noffke, who ended with 3-62.
Riki Wessels made 39 off just 36 balls before edging a Jim Allenby delivery behind to wicketkeeper Mark Wallace.
Dalrymple, who went to 50 off 114 balls, then shared the day's main partnership of 71 with Mark Wallace (48).
Mark Turner caught Mark Wallace off his own bowling in between, giving Somerset an early grip on the contest that they refused to relinquish.
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But the Dragons had enough ammunition left in the locker as Hemp (34), Dalrymple and Mark Wallace (26 not out) got the visitors home.
Stand-in skipper Mark Wallace then turned to seam but, when he decided to take the second new ball, Middlesex only required 10 more to win.
The former pupil of Pontarddulais Comprehensive School provided a third catch for wicket-keeper Mark Wallace by finding the edge of Will Rudge's bat for his seventh wicket.
On a pitch that offered little encouragement to the Glamorgan seamers, off-spinner Croft was introduced less than an hour into the day's play and should have had Cook stumped on 27 only for Mark Wallace to fluff his lines.
Bourgoin hit back with their first try on 57 minutes as captain Julien Frier powered through flimsy tackles by Wallace and Mark Bartholomeusz, before offloading to Tchougong, who trundled over from 10 yards.
Tries from Paddy Wallace, Darren Cave and Mark McCrea helped Ulster into a 22-6 lead at the break.
"We went out and gave it our all and our defence played well to keep Wallace out for the whole match, " added captain Mark Jones.
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