McAuley Lacey opened up a score on the away side, but despite Iceton's equalising Isaac Suns, George Pearson tried to send the league leaders with a 2-1 halftime lead.
The Suns doubled the tally early in the second half before Zack Hansen became the lead for the first time.
But Amosabee attacked Matty Jackson almost immediately before Oliver Touse scored a very important winner and handed the points to the away side.
Elsewhere in the division, Goalsport and Snineton had a peaceful North-core draw at George Pinder.
The only excitement in the note was a save from Brad Cawkwell's spot kick, preventing the host from sealing off three valuable points.
Goldsborough edged 4-3 with his fun Panasonic Cup first tie on his fellow Division 2 side Sinnington 4-3.
Ben Watson's hat-trick and Ben Duel Strike deal the ultimate damage to Goldsborough within the opening half, but Sinnington creates the game with Jack Vincent's reply and Charlie Hancock's free-kick braces But that wasn't enough to force a penalty shootout.
There was contrasting fortune as Thorntondale and the Wombleton Wanderers took them to the field of the Scarborough District Cup.
Wombleton came on top with a tie at the seamer. Dun Marshall grabbed all the goals on the Ryedale side in a 4-2 victory.
However, Morgan Elven's late hat-trick wasn't enough for Dale as he was beaten 4-3 at Franborough.
Scarborough's Junior Cup pited the Amotherby & Swinton reserve against Slingsby for the second time in eight days.
The home side took the lead in the first half through Captain Alex Kroll, and their advantages doubled thanks to the Charlie Levis strike in the second season.
Slingbee halved the deficit before Levis turned into a villain and gave visitors the opportunity to equal off 12 yards. However, keeper Riley Howe came to the challenge and saved him wisely.
With time ticked, Slingbee threw everyone, including the keeper, for a late corner kick, including the keeper, but the host cleared, and Kianstead lace up the other side of the field Scoring to the empty net and ensured the next progression on his side round.
Heslerton went back to the semi-finals with a comprehensive 3-0 victory at Ridal Sports Club.
Visitors welcomed influential midfielder Jamie Atkinson after a two-game absence due to injury, and gave him a comfortable lead in the after-goal break from Morgan Kendrew and Matty Bean.
They added a third just before the time mark. This is a great right foot finish from the edge of the Sam Besau box.
Ryedale saw more balls in the latter stage, but the visitors were not in the mood to even admit comfort.
Elsewhere, it was a long journey for Bagby & Barbo as they were slapped 6-1 at Westpier.
Bagby's only goal came from Louis Chapman in a match where the hosts saw Run Riot.
