Havant controlled the game tactically from the first whistle, but it was not until the 30th minute that Avery, picking up a quick pass from Peter Nail, outwitted the Hounslow defence to flick home the winner.
East Grinstead moved into third place with goals from Richard Gibson (2), Stuart Head and Phil Wallis in a 4-2 victory at Bournville as Reading went down 4-2 to Old Loughtonians at Chigwell. After a goal in 11 seconds from Jon Wyatt put the Berkshire side ahead the Old Boys took over with two goals from Paul Krishman and one each from Nick Thompson and Brett Cooper.
The biggest win of the day was Southgate's 6-1 feast away to Welton, with Sean Kerry scoring three times.
In the Second Division, Surbiton, 3-0 winners at Doncaster, moved four points clear at the top as Guildford could only manage a 1-1 draw with Barford Tigers.
In Spain, England's women took the silver medal in the European Under-21 Indoor Nations Cup, drawing their last game 4-4 with Spain, who won the gold. After trailing 4-0 at the interval, Lucy Cope, the captain, scored a second- half hat-trick, with Jackie Savage completing the scoring. Earlier in the day England had beaten France 5-0, Cope and Anna Bennett each scoring twice.Reuse content