Thorpe, top scorer with 90 in the second Test victory over West Indies earlier this week, top-scored again with 88 while Jones made 66 as England made 347 in their first innings, a lead of 218.
In reply, the Carib Beer XI were 51 for one at the close, 167 behind.
Resuming on 121 for three, Test wicketkeeper Chris Read, in the side as a specialist number five batsman, fell for nine.
But Thorpe and Jones then added 117 for the fifth wicket before the left-handed Thorpe was caught off medium-pacer Tonito Willett. He hit eight fours and one six.
Jones recovered from an uncertain start, smashing five fours and three sixes before he was the first of four victims for fast bowler and West Indies Test hopeful Jermaine Lawson.
All rounder Rikki Clarke plundered 35 while Ashley Giles made 22.
In reply, James Anderson gave England the perfect start when he removed Xavier Marshall for four.
But Carib XI captain Daren Ganga, drafted into the West Indies Test squad on Saturday as cover for Devon Smith who has a finger injury, survived on 17 not out while Sylvester Joseph made a quick-fire 25 not out.
Carib Beer XI first innings 129 (M.Hoggard 4-27)
England first innings (overnight 121-3)
M.Trescothick b Banks 50
M.Butcher c Marshall b Washington 17
P.Collingwood st Ramdin b Mohammed 20
G.Thorpe c sub b Willett 88
C.Read c Ramdin b Mohammed 9
G.Jones c sub b Lawson 66
R.Clarke c Joseph b Lawson 35
A.Giles c Ramdin b Lawson 22
G.Batty lbw b Lawson 0
M.Hoggard b Mohammed 10
J.Anderson not out 1
Extras (b-8 nb-21) 29
Total (all out, 102 overs) 347
Fall of wickets: 1-30, 2-72, 3-120, 4-142, 5-259, 6-285, 7-325, 8-325, 9-336
Bowling: Lawson 29-3-94-4, Washington 6-0-15-1, Rampaul 18-3-58-0, Mohammed 28-1-114-3, Banks 9-3-22-1, Bravo 5-1-22-0, Ganga 4-1-9-0, Willett 3-0-5-1