The visitors wasted little time after kickoff to stamp their authority on the match and they could have opened the scoring inside two minutes through Reece Styche, but his low shot was well kept out by Daniel Lloyd-Weston.
Southport finally got hold of the ball just before the quarter-hour mark and Richard Brodie could count himself unfortunate not to break the deadlock when his driven shot just evaded the post with goalkeeper Danny Lewis beaten.
The home side built on that opening and after 25 minutes, they took the lead when Connor was on hand to fire home from close range after the ball had dropped to him from a corner.
Kidderminster, who were looking to keep hold of their early unbeaten record, almost found an immediate response through Kevin Nicholson, but his free kick from the side of the area was diverted wide.
Craig Reid forced Lloyd-Weston into another fine intervention moments before the half-time whistle, but Southport hung on to hold an advantage after the opening 45 minutes.