Leigh Franks powered home a diving header from Sam Cook’s set piece to hand United the lead.
Cameron Dobson then netted a free-kick to ensure that the away side went into half-time with a two-goal cushion.
Hunmanby remained in the ascendancy after the interval, and Dobson struck again to round off a fine team display from the victors.
Sean Exley marked his league debut for West Pier with five goals as the reigning champions ran riot at home to Westover Wasps.
The striker, who signed the club in the close season from Pier’s title rivals Newlands, was joined on the scoresheet by brothers Gary and Neil Thomas, who both hit hat-tricks.
Strikes from Sam Garnett, Niall Gibb and Martin Cooper, plus an own goal, sealed a 15-0 win in a one-sided affair.
Edgehill were another side to get off to a winning start when they triumphed 6-1 on the road at Cayton Corinthians.
Joe Gallagher moved Steve Clegg’s men ahead after 20 minutes, and Wayne Aziz doubled the lead 10 minutes later.
Aziz netted again 10 minutes into the second period before Dean Craig converted from the penalty spot and Gallagher hit his second of the afternoon.
An 85th-minute own goal took the Edgehill tally to six, while Isaac Sands managed to pull one back for the Corinthians.
Two-goal Gallagher was singled out by boss Clegg after a commanding display in the centre of midfield, with Aziz and new recruit James Gunn also impressing.
New Seamer Sports boss Joe Wright earned a point from his first game in charge, a 2-2 draw with Whitby Fishermen.
Danny Glendinning and Gary Lawton were on target to make sure that Wright, who has stepped up from managing the club’s reserve team, ended up with a share of the spoils.
Phil Raisbeck and Neil Hart registered for the Fishermen.
Newlands Park eased to a 6-0 success on the road at Sleights.
Drew McCoubrey led the way with a four-goal haul, while Dan Freer also struck and Tyler Richardson sealed a fine debut performance by finding the net.