Joe O'Neill's stoppage-time goal eventually broke the deadlock and made it five successive wins. A controversial goal kick, awarded when Eastwood thought they should have had a corner, found O'Neill, whose shot from just outside the area beat John Danby.
The closest Eastwood came to scoring was a header from Russell Cooke which struck the bar.
Guiseley are looking to climb above second placed Boston United in tomorrow night's rearranged league game at Nethermoor in readiness for the daunting home FA Cup first round tie against Crawley Town on Saturday.
Harrogate Town gained a valuable 1-0 win at Redditch United courtesy of captain Steve Bowey's first goal for the club.
Graeme Armstrong had Harrogate's best first half chances, shooting wide when through before lobbing over an open goal.
Redditch went close when Phil Green's shot hit the crossbar.
Harrogate took the lead on the hour when Bowey netted from Lee Ellington's flick on.
With 10 minutes left, Marlon Walters was dismissed for a foul on Harrogate's Wayne Phillips.
A late save by debutant goalkeeper Mark Cook ensured Harrogate won.
FA Trophy Second Qualifying Round: Whitby recovered from the shock of conceding a second-minute goal to defeat visitors Clitheroe 3-1.
Ashley Parillion headed Clitheroe into their early lead but Tony Hackworth equalised with a low shot in the 29th minute and second half goals in a two-minute spell from Dave Southern and Chris Batchelor carried Whitby through.
Kevin Ryan's 32nd-minute goal gave Harrogate Railway Athletic the advantage at Romulus, who had substitute Naveed Arshad sent off for an aerial challenge. Phil Male equalised with eight minutes left but Railway got up a head of steam and Michael Duckworth's low shot brought their 89th-minute winner.
Stocksbridge Park Steels overcame a strong challenge from visitors Rugby and triumphed 3-2. Richard Haigh and Andy Ring built a two-goal lead for Steels and after Luke Keen and Nik Preston pulled Rugby level, Ring netted the stopapge-time decider.
FC Halifax Town were beaten 2-1 at Curzon Ashton where all three goals arrived in the second half. Chris Worsley headed the home side into a 54th-minute lead, Jamie Vardy nodded a 70th minute equaliser but Dan Broadbent conjured an 83rd minute winner for Curzon.
Ferriby fire back
Evo-stick: North Ferriby conceded two penalties but overcame visitors Ashton United 3-2 in the Premier Division.
Paul Harsley, Chris White and Alex Davidson scored the goals that earned the points, Aaron Burns twice keeping his cool to score from the spot for Ashton.
Frickley Athletic were 3-2 winners at Bradford Park Avenue where Steve Burton opened the scoring from the penalty spot for the home side. Mark Whitehouse and Andy Lee nudged Frickley ahead before the interval and Ashley Longstaff made it 3-1 before Adam Clayton scored with five minutes left.
Ossett Town made it five games without a win as they went down 2-0 at Buxton.
Wakefield fought out a 1-1 draw against Warrington in Division One North. Tom Denton headed Wakefield into the lead just before half-time but Chris Gahgan levelled.
Bambrook spot on
NORTHERN COUNTIES EAST: Farsley came from behind to beat champions Bridlington Town 2-1 and open a five-point lead at the top of the Premier Division.
Parkgate moved up to second place even though they could only draw 1-1 at Brighouse Town.
Craig Palmer fired Bridlington in front after 14 minutes and it took the leaders until the hour mark to reply, James Knowles netting. The match was decided with 14 minutes to go when Simeon Bambrook fired home his third penalty in as many matches.
Lee Burgess put Brighouse into a first-half lead but Luke Fletcher rescued a point for Parkgate with five minutes left.
Pickering were again on a goal spree, hammering Dinnington 5-1 with strikes from Tom Adams, Josh Greening, George Rose, Darren Clough and Glen Dinning.
Danny Kemp, Rob Northen and Richard Dunning were on target as Scarborough beat Armthorpe.