Hoskins' first came 28 minutes into the contest, with the hosts adding to their tally in the 59th minute through Appere and 63rd minute through Hoskins again to put the result beyond doubt.
Despite the loss, results elsewhere left Town mathematically safe from relegation and set for a third season in SkyBet League Two.
Simon Weaver made three changes from Good Friday's defeat as Josh Austerfield, Rory McArdle and Simon Power came into the starting line-up, replacing Alex Pattison, Ryan Fallowfield and Mark Beck.
Northampton struck woodwork in the sixth minute as Captain Fraser Horsfall met a corner and headed onto the crossbar, almost claiming his ninth goal of the season.
Harrogate were dealt another cruel injury blow midway through the first half as Will Smith went down when chasing the ball with what looked like a knee injury, Leon Legge taking the defender's place.
The hosts took the lead in the 28th minute when Ali Koiki's diagonal bass was worked back across goal to Hoskins arriving late into the area with a low finish.
Town's best moment of the first half came after some good wing play from Simon Power set up both Luke Armstrong and Josh Austerfield, though both attempts were blocked.
The half ended with a couple of Louis Appare attempts on goal, though neither attempt from the Cobblers striker troubled Joe Cracknell.
Appare was involved again after the restart, shooting low after a quick turn, though Cracknell got down well to save.
The Cobblers forward finally got his name on the scoresheet just before the hour mark, latching onto Legge's backwards header ahead of Cracknell and walking the ball into an empty net.
Hoskins' second of the game put the result beyond doubt in the 63rd minute, Appare the provider this time as his through ball set his teammate one on one with Cracknell and able to beat the Town stopper.
Shortly after the game was momentarily halted by a drone flying over Sixfields, Jack Muldoon had the chance to pull a goal back with just over 15 minutes to go when he was released by Power, but could only fire into the side netting.
Aaron Martin was introduced in the closing stages and came as close as anyone in blue to getting on the scoresheet, forcing Liam Roberts into a save at his near post, in the last goalmouth action of the afternoon.
Town: Cracknell, Smith (Legge 23), Burrell, Thomson, Sheron, Muldoon (Martin 75), Austerfield, Diamond, McArdle, Armstrong, Power
Subs not used: Beck, Ilesanmi, O'Boyle, Giles
Booked: Austerfield, Burrell
Northampton: Roberts, McGowan, Sowerby, Guthrie, Horsfall, Hoskins (Pollock 86), Pinnock, Koiki (Mills 86), McWilliams, Eppiah (Zimba 77), Appere
Subs not used: Harriman, Kanu, Maxted, Rose
Goals: Hoskins 28, 63, Appare 59
Referee: R Lewis
Attendance: 5,160 (93 away)