With home advantage in their quarter-final against Nottingham Forest, to be played next Tuesday, they must be short-priced favourites to make further progress.
As at Yeovil on Saturday, Arsenal's attitude was exemplary. Again the opposition, and the conditions, spelled upset. Again the Premier League side applied themselves diligently to ensure that there was never going to be one.
Scarborough, vigorous and determined, made it a hard night's work for George Graham and his team, and deserved the consolation of record receipts of some pounds 37,000.
They had billed it as the biggest match in their brief history, but the weather did its worst to ruin the occasion. The Fire Brigade's efforts to pump a waterlogged pitch into something like a playable state nearly came to naught when the fog came swirling in off the Vale of York.
With visibility deteriorating by the minute throughout the first half, Keith Hackett must have spent the interval pondering the wisdom of his decision to start the game. Ian Wright could have stuck up any number of fingers and no one would have known.
To the referee's enormous relief, the freezing grey blanket lifted in the second half to banish the grim prospect of abandonment.
Scarborough closes down in midwinter, and it takes something extra special to bring the ghost town back to life before the Easter influx. The Big Match, as everyone locally was calling it, was big enough, and tickets changed hands at 10 times face value.
Money wasted. Of the 6,261 in attendance, no more than the odd 261 can have had a decent view.
It was a hard match to watch, in every sense. Out in the murk it was just possible to discern Darren Foreman shooting in early on from an offside position. The referee did well to spot the flag. Linesman? What linesman?
Arsenal had been first to show - a misnomer if ever there was one. The invisible man, rumoured to be Wright, headed narrowly wide from Anders Limpar's left wing cross.
Scarborough's immediate response saw John Ashdjian's shot cleared off the line by the man with the X-ray eyes, Lee Dixon. Tommy Mooney was too close for David Seaman's comfort after 33 minutes with a rising 20-yarder which would have caused a ripple of excitement had more than a privileged handful been able to see it.
Wright, supplied by Smith, tried to repeat his chip at Yeovil on Saturday just before half-time, but the mire ruined his contact, and Stuart Ford saved easily.
Smith was again involved in a supporting role after 51 minutes, when Arsenal's goal was a nice mixture of skill and strength.
Winterburn played a neat 1-2 off the tall targetman before powering through Simon Thompson and rifling the ball home, left- footed, from 15 yards.
Scarborough: Ford; Thompson, McGee, Lee, Ormsby, Curran, Ashdjian, Himsworth, Mooney, Foreman, Lightbourne (Jules, 62). Substitute not used: Mockler.
Arsenal: Seaman; Dixon, Winterburn, Hillier, Bould, Adams, O'Leary, Wright, Smith, Merson (Campbell, 88), Limpar. Substitute not used: Jensen.
Referee: K Hackett (Sheffield).
Blackburn v Ipswich or Sheffield Wednesday
Crystal Palace v Arsenal or Nottingham Forest
First leg week of 7 Feb; second leg week of 8 March