Gate lost their opening Hallmark Security League fixture in Stoke, where they trailed 3-0 after 25 minutes.
The Marton club’s longest journey of the season in the premier division came on the opening day and they made a bright start before conceding three goals in nine minutes.
Neville Thompson was allowed too much space inside the box to open the scoring after 16 minutes.
The second followed on 21, when Dan Cope was first to a cross from the left and was not closed down.
And four minutes later it was 3-0, Hanley counter-attacking quickly from a Gate corner before Theo Stair fired past keeper Ben Fletcher.
It could have been even worse for Gate a minute later but Fletcher tipped Cope’s effort over the bar and the resulting corner was headed wide.
Gate steadied the ship until half-time and began to create chances after the break, when Nick Greenall’s looping header was saved and Paul Carroll shot wide at the far past.
On his full debut, Dean Ing stung the keeper’s gloves on the hour with a shot from outside the box.
Gate player-boss Danny Penswick was denied by the keeper five minutes later, then at the other end Thompson fired narrowly wide as he looked for his second.
Cope, however, was not to be denied a brace and completed the scoring with the final kick of the game, a shot on the turn following a poor Gate clearance.
Having exited the FA Cup by the same scoreline against Ashton Athletic a week earlier, it’s an unhappy start for the new committee in charge at Gate, who are away again on Saturday to newly promoted Charnock Richard.
Gate: Fletcher, Carroll, Moorhead, Penswick, Douthwaite, Hall, Greenall, Ing, Dawson, Buchan, Moxon. Subs: Smith, Colquhoun, Green.