Emeka Obi’s 74th-minute header was enough to win a tie that sparked into life in the second half.
Ast expected, manager Jim Bentley made several changes to the team that had won at AFC Telford United in National League North a week earlier.
Liam Nolan, Jack Sampson, Ethan Walker and Jordan Hulme all came into the starting XI, with Nick Haughton on the bench.
Goalkeeper Chris Neal was also back in the squad among the substitutes, with Bobby Jones making his second start in goal.
The game started quietly, with neither side having an opportunity in the first 10 minutes.
The first chance fell to Coasters striker Jack Sampson, whose fantastic header from a Luke Joyce free-kick was tipped over by Jacob Chapman in the Gateshead goal.
Bentley’s side had a let-off as the game approached the 40-minute mark, when Adam Campbell burst down the right and squared the ball for Paul Blackett to finish but the referee's assistant deemed him to be offside.
The disallowed goal spurred the visitors on, and when Ryan Wombwell's cross reached Connor Pani on the penalty spot, his clever backheel went straight into Jones' hands.
The Coasters had a spring in their step at the start of the second half.
Walker, making his first start since rejoining the club on loan from Preston North End, floated the ball towards fellow loanee Kieran Lloyd at the back-post.
The full-back from Wigan Athletic played the ball inside, where the white shirts were lining up, but Chapman got down well and claimed.
There were chances for both sides, and the Heed were next to go close as Robbie Tinkler met a free-kick from the left and forced Jones to spring across his line and make a superb save to his left.
Campbell was next to try his luck for the visitors with a curling effort towards the far post, though Jones got down and held well.
Despite Gateshead’s best efforts, the breakthrough came for the Coasters when defender Oki towered above everyone to find the top corner with a header from a corner by substitute Haughton.
The Tyneside club searched for an equaliser but Louis Storey fired a fierce shot just wide and Fylde again kept Gateshead at bay, as they had in last month's 2-0 league win.
Fylde: Jones, Lloyd, Obi, Stott, Conlan, Joyce, Nolan (Philliskirk 75), Osborne, Walker, Sampson (Haughton 68); Subs not used: Neal, Tollitt, Byrne
Gateshead: Chapman, Tinkler, Wombwell, Storey, Forbes (Nicholson 25), Jacob, Pani, Hunter, Williams, Campbell, Blackett (Scott 75); subs not used: Bailey, Olley, Ward.
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