Moody made 74 of his 131-ball century in boundaries, allowing Philip Weston (145no) to play more sedately and reach his century in 228 balls, with 10 fours and a six. David Leatherdale then added 63 not out for his part in a continuing fifth-wicket stand of 120 with Weston.
At Northampton, the hosts had Tony Penberthy (65) and David Ripley (92) to thank for taking them towards 310 for 7 against their neighbours Leicestershire. The sixth-wicket pair put on 155 in all, after coming together at 105 for 5.
Jason Pooley fell just two runs short of his century as Middlesex took charge against Nottinghamshire at Lord's. Their captain Mark Ramprakash made 55, and the hosts finished the day on 283 for 5.
Somerset restricted Durham to 230 all out at Chester-le-Street, despite 79 from John Morris, and then responded with 75 for 1.
On a day that saw five individual centuries struck around the country, bottom-of-the-table Sussex mustered just 114 between them against Hampshire at Southampton. Stuart Milburn took 4 for 38, and the former England off- spinner Shaun Udal 4 for 17. Hampshire ended the day on 185 for 2, with Giles White and Paul Whittaker (both 68no) enjoying an unbroken third- wicket stand of 114.