The home side opened the scoring on 17 minutes through Joe Dalton's superb finish, but Ben Luntley soon levelled thanks to a header by Ben Luntley from a good cross by Brad Wood.
Yarm restored their lead three minutes before half-time when Jack Dalton nipped in to slide his shot past Cammish.
The Newlands keeper made a crucial save on the stroke of half-time, superbly tipping over a fierce goalbound shot from Joe Dalton.
Newlands levelled from the penalty spot after Matty Dixon fouled Luntley, Dan Freer slotting home from the penalty spot.
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In the shoot-out, the Newlands scorers were Luntley, Freer, Cammish, Robbie Scarborough, then Cammish saved Yarm's fourth and Drew McCoubrey slotted home the visitors' fifth to seal the win.
Kile Fields, managing in the absence of boss Paddy Mancrief, singled out Jack Hakings as man of the match in a great team effort.
Edgehill went out of the cup, a depleted visiting side putting in a great effort despite suffering a 3-2 loss at Huntington Rovers.
Ten minutes before half-time Max Wright played a ball towards Joel Ramm, it looked like the defender would clear but he slipped letting veteran Ramm run clear and he calmly slotted under the Rovers keeper, ex-Edgehill gloveman Liam Giles.
A minute before the break Rovers got their deserved equaliser from a corner, the ball deflecting past helpless keeper Sean Exley.
Ten minutes into the second half Edgehill restored their lead when Ryan Link brilliantly headed home a Wright cross.
But within two minutes Rovers scored again, the striker tapping home from a pull back.
In the 88th minute Rovers got the winner, despite claims of offside the referee gave the goal.
Man of match on his 40th birthday was Wayne Aziz followed closely by Tommy Wilson, while Liam Coulson impressed in his first 90 minutes in two years after breaking his leg.
West Pier were handed the win as their visitors Strensall Tigers conceded, while Itis Itis Rovers conceded their game at Wigginton Grasshoppers.
Filey Town romped to a 9-1 win at Scalby in the Scarborough Saturday League first division.
The opening 45 minutes was a close contest, Town leading 2-1 at the break, George Wilson notching for Scalby.
Man of the match James Pinder banged in a hat-trick on his return to the club from now defunct Hunmanby United, with another ex-United man, Olly MIlner, scoring two great finishes from the right wing.
Joe Gage, Tyler Beck and Liam Sugden also netted one apiece, an own goal completing the rout.
Man of the match for Scalby was Max Edwards.
Seamer Sports Reserves hot-shot Chris Stubbings scored four goals in his side's 8-3 home win against Newby in Division Two.
Man of the match Stubbings shone, with player-boss Connor Myerscough also scoring a brace, Tyler Duckworth also grabbed a goal along with Tom Greenwood
Joe Messruther also impressed with a cameo performance, showing a great range of passing and tidy footwork
Luqa Borg, Luke Foster, and Keith Savage netted for the visitors, with the man of the match split between Foster and Stu Wallace.
West Pier Reserves, who included three members of the McNaughton family, most notably Selby Town and former Scarborough Athletic striker Flynn McNaughton, romped to a 13-1 win at Goal Sports on Friday night at the Flamingo Land Stadium.
Flynn McNaughton led the way with four goals, come on at half-time with Pier already 7-1 ahead. There were also braces for Benny Davis, Mikey Hartnett, Martin Cooper and Archie McNaughton, plus a Sam Garnett effort. Dempsey Stubbings notched for Goal Sports.
Pier boss Will Jenkinson said: "It was great to see three McNaughtons all on the pitch playing together, it must have been a proud moment for dad Mike to play alongside his lads.
"The lads played very well and I was really proud of the younger lads I thought they all did brilliantly."