Rosette led 2-0 before Mark Bean halved the deficit for Westover.
The away side notched again though to take a 3-1 lead before Noah Young smashed in a brace to turn the game on its head and make it 3-3.
Rosette must’ve thought they’d won it when they won a penalty, but the resulting kick smashed off the bar and away to safety.
Wasps took full advantage and Jack South’s perfectly-weighted ball over the top found Callum Myers, who made no mistake in winning the contest for Rob McPherson’s men.
McPherson singled out two-goal hero Young, but paid tribute to both sides following a feisty but fair cup clash.
There was extra-time heartbreak for two Whitby-based sides, Whitby RUFC and Sleights Reserves, as they both threw away leads late on in normal time before losing in extra-time.
Whitby RUFC led Filey Town 1-0 thanks to a Lewis Peel strike after 30 minutes, but a last-minute penalty from Darren Clough denied them their place in the next round.
Town smashed in two extra-time strikes to make it 3-1 before James Organ-Simpson ran the full length of the pitch before firing in a fine solo effort to make it 3-2.
Town weren’t to be denied though and another late penalty sealed their spot in the draw for the next round.
Sleights Reserves also suffered an extra-time defeat as they went down 5-3 on the road at Scalby Reserves having led 3-1 with nine minutes left thanks to goals from Rich Davies, Mike Butler and Mike Brennan.
Scalby, who had to come from behind to go in level at half-time thanks to a Karl Hansell goal from a free-kick, found themselves 3-1 down after 81 minutes.
A George Wilson penalty and a last-gasp leveller by sub Dave Oxley took the game into extra-time and the Otters took control.
Wilson calmly converted another penalty before the break, and Daniel Gregory lifted over keeper David Fish with the last kick of the game to secure a 5-3 victory.
Nic Wheatman and James Blenkinsop stood out for Jeff Brader’s side.
Scalby’s first team romped to a 10-2 win at West Pier Reserves to move into the next round.
Shaun Scales was Scalby’s star man as he fired in a brace and set-up six of the Otters’ goals, while Liam Vasey, Dan Peel and Mike Hartnett all grabbed a brace apiece.
The scoresheet was wrapped up with goals from Elliot Spurr and Ashley Townley, while Pier’s goals came courtesy of a Dave Crawford penalty and a Steve Paxton strike.
Duchess romped to a 7-0 win at struggling Snainton.
Adam North and Craig Sherwin both fired in doubles and there were also goals for Tom Hicks, JP Watson and James Hughes.
Chris Ryan was Duchess’ star man.
West Pier cruised to a 13-0 win against Commercial.
Billy Logan hammered in five for Andy Spivey’s men, while Gary Thomas fired in hat-trick and his brother Neil grabbed a brace.
Martin Cooper, Will Jenkinson and Shaun Dodson rounded off a comfortable afternoon for Pier.
Seamer go into the next round after they battled back from going behind to beat Westover Wasps 5-1 at Oliver’s Mount.
Paddy Parke’s men went behind after Adie Blake conceded a pen and Chris Hannam slotted home.
It only took five minutes for the away side to level matters up though, Gary Lawton’s free-kick finding Luke Delve, who made no mistake finding the back of the net.
Delve smashed in shortly after the break to put Seamer in front, before goals from Joe Gallagher, Rob Speight and Danny Bradbury wrapped up a 5-1 win and a place in the next round for Seamer.
Parke singled out Lawton after a fine performance on the left flank.