United opened the scoring against the run of play in the first half, but just before half-time Harry Holden's cracking finish brought the scores level.
Fine work from Danny Kelly down the right wing saw him send a cross into the penalty area after the interval, with United player-boss Leigh Franks sending the ball past his own keeper.
The visitors then levelled when a free-kick broke to James Pinder to net a second United goal.
Seamer keeper Jordan Wood then pulled off a superb late save to take the game to penalties, and, after both sides' first four penalty-takers converted, Wood saved brilliantly again and player-manager Tommy Adams fired home to seal the win.
Kelly, Price, Gaz Lawton and Kris Tate were the first four successful spot-kick kings for Seamer, with Josh Lewis their man of the match.
A depleted Filey Town side had to work hard for their 4-3 win at Newlands.
Joe Gage opened the scoring for the visitors, only for Lee Cappleman to level before half-time.
Joe Gage restored the lead after the break, with Ash Robinson and Luke Burton also notching before Newlands launched a late comeback through goals from Dan Freer and Michael Wilson, forcing Town to hang on for the win.
Joe Gage and his brother Max were the star men for Filey, with Lee Micklethwaite also pulling the strings in central midfield.
Itis Itis Rovers had a much easier time in their tie at home to second division Ayton, easing to a 5-1 home win.
Player-manager Mikey Barker lobbed in from the edge of the area to put Rovers in front early on, then Curtis Ireland's fierce strike and a Neil Forsyth effort made it 3-0 at the interval.
Two superb Ryan Matson goals after the interval pulled Itis Itis further clear, his first a superb first-time shot from the centre-circle after the Ayton keeper's clearance fell straight to him and the second an excellent finish from the wing after winning the ball from the visiting gloveman.
Tyler Beck pulled a goal back for the hard-working Ayton team, whose man of the match was Jaymaine White, Jack Ramos earning the man of the match award for Rovers from the heart of their midfield.
Edgehill Reserves powered to a 7-0 win at Beckett League outfit Rosedale in the Scarborough & District FA Junior Cup.
Callum Myers continued his rich vein of form in front of goal with a hat-trick, including two penalties, while Stephen Whitaker headed in the opener and Tyler Richardson smacked in a 25-yard free-kick.
Goals from Andy Noon and Marcus Mockridge completed the scoring for the visitors, with defender Anthony Pickles named as their man of the match.
Seamer Sports Reserves claimed a 7-4 win at FC Rosette in an action-packed encounter.
Ben Mason and man of the match Jordan Glendinning scored two goals apiece for Seamer, with Daz Hastie, Callum Plant and a cracking long-range strike from Cameron Myerscough completing the scoring for Paul Greatorex's side.
Man of the match Dane Robinson, Danny Thompson, Joe Rose and Tommy McDonald were on target for Rosette.
Cayton Athletic slipped to a 4-3 home loss against Beckett League side Lealholm.
In the opening exchanges, a spot-kick was given to Cayton after Josh Venner was taken down in the box but Macauley Riley had his penalty saved.
The visitors then scored from a setpiece and then a shot from outside the box.
After that keeper Steven Robinson had to go to hospital after being injured in a collision with the Lealholm striker.
The home side then pulled a goal back, when from a Freddie Schmuck corner, man of the match Adam Smith got to the ball first to score.
Lealholm started strongly after the break, with a Sam Raper own goal another effort saw them lead 4-1.
Cayton came back into it with a Venner goal and an own goal, but the visitors hung on to progress.
West Pier Reserves suffered a 6-3 loss at Beckett League side Sleights, Zak Hansen scoring twice for the visitors.
Man of the match Taylor Jordan was named as man of the match for a strong display in midfield.