Allan Lamb had chosen to bat in overcast conditions and was one of the batsmen to fall to the fast bowler as his side collapsed to 50 for 6 and only a determined rearguard action mounted by Tony Penberthy enabled the visitors to reach a modest 164.
Penberthy battled for more than three hours for his undefeated 56 and was the only batsman to stand in Connor's way for long. Connor bowled 26 overs and his haul was his second-best of an 11-year career.
In reply, Hampshire lost Paul Terry in the second over to John Hughes. A stand, though, of 53 for the second wicket between Giles White and Tony Middleton enabled them to overcome the setback, White going on to make 38.
Robin Smith now joined Middleton, but Hughes returned to take two wickets in the penultimate over of the day. He had Smith caught at slip by Lamb for 23 and then dismissed the nightwatchman Raj Maru for a duck to leave Hampshire struggling at 87 for 4 by the close.
While Cheltenham proved a graveyard for Yorkshire on Monday, Mark Benson played a captain's innings when Kent dropped in. Benson helped raise 209 for the first wicket and went on to bat four and a half hours for 159.
When he fell to the medium pace of Mark Alleyne, however, it began a collapse which saw eight wickets go down for 64. Alleyne was twice on a hat-trick as he returned a career-best 5 for 78 off 14.2 overs, Gloucestershire dismissing their visitors for 360.
As for the injury-hit Yorkshire, they lost two wickets in the last half-hour to undermine a strong position of 267 for 4 away to Durham, finishing on 298 for 6 with Richard Blakey unbeaten on 50.
After Somerset had lost their openers to a fiery spell by Ottis Gibson at Swansea, Andy Hayhurst came up with the captain's perfect answer of a battling innings. Hayhurst finally reached his century in 286 minutes, Somerset closing on 257 for 4 and Hayhurst still there on 105.Reuse content