The Lions were dealt a blow before kick-off with first-choice goalkeeper Steven Drench ruled out due to illness.
But young ex-Leeds United keeper Dan Atkinson donned the gloves and delivered with a number of fine saves.
Alty’s Josh Ginnelly had the first big chance of the game but fired a well-hit shot which Atkinson saved smartly to keep the scores level.
Guiseley started to attack themselves with Adam Smith hitting an effort which took a big deflection and wrong-footed the goalkeeper but the ball hit the post.
The Lions had another chance when Liam Dickinson passed to Nicky Boshell who saw his goal-bound effort blocked.
But the hosts got the first goal when Michael Rankine used his strength to get past two Guiseley defenders before powering an effort past Atkinson.
Guiseley started the second half well with Boshell again going close as the away side pushed forward.
And the away side were soon celebrating when Rob Atkinson was found by Smith from a corner and the big defender headed the cross into the back of the net.
On a pitch that was cutting up badly, Guiseley went close to taking three points when Danny Lowe delivered a dangerous cross which was nearly put into his own goal by Gianluca Havern.
The Lions now sit 17th and return to action tomorrow evening at home to second-placed Forest Green.
FC Halifax Town moved out of the drop zone with Saturday’s 4-2 success at home to third-placed Grimsby Town.
Three goals in 20 first-half minutes from Billy Whitehouse, James Bolton and Nicky Wroe put Town in control before Jake Hibbs added the late gloss.
The Shaymen now sit fifth-bottom and return to action tomorrow evening at ninth-placed Braintree Town.
In National League North, second-placed Harrogate Town further cemented their promotion push with a 5-0 blitzing of CNG Stadium visitors FC United of Manchester.
Town lost Warren Burrell to a straight red card for a heavy challenge in the first half but cruised to victory with goals from Brendon Daniels, Jordan Thewlis, Jack Emmett, Paul Clayton and Joe Colbeck. Town return to action return to action on Saturday at home to 12th-placed Gloucester City.
Bradford Park Avenue sit five points above the drop zone in 15th after Saturday’s 3-0 loss at Lowestoft Town. Avenue host sixth-placed Boston United on Wednesday.
OSSETT TOWN moved five points clear of the Evo-Stik League’s First Division North drop zone with a fine 2-1 success at promotion-chasing Burscough.
Seventh-placed Burscough could have moved to within two points of the play-offs with a victory and looked on course to achieve exactly that when Paul Williams gave them a 15th-minute lead.
However, Danny Frost levelled matters eight minutes before the interval and Town were then handed a potentially crucial win thanks to Alex Peterson’s strike three minutes after the hour.
Third-bottom Town then learned that second-bottom Harrogate Railway had been undone by a last-minute penalty in a 2-1 loss to visiting Bamber Bridge. Daniel Thirkell’s strike after 54 minutes had Rail’ on track for victory but Matthew Kay levelled with 11 minutes left.
Jamie Milligan’s 90th-minute spot kick provided a late kick in the teeth for the hosts.
At the other end of the table, Danny South grabbed the only goal of the game as Ossett Albion maintained their play-off push with a 1-0 success at home to fifth-bottom Scarborough Athletic.
South sank the Seadogs with his effort six minutes after the hour which leaves Albion in fourth place.
Brighouse Town, though, were blitzed 4-0 by third-placed visitors Spennymoor Town while Farsley Celtic’s trip to Witton Albion was postponed.
In the Premier Division, Frickley Athletic moved 10th with a 3-0 triumph at home to Skelmersdale United.
The home side’s Luke Hinsley, Bradley Grayson and Jacob Hazel all bagged a goal apiece.
Sixth-bottom Whitby Town, though, were felled 1-0 at Granthan Town whose Daniel Meadows netted a 74th-minute penalty. In First Division South, Goole AFC were felled 1-0 by visiting Chasetown whose Paul Sullivan bagged the winner.
TADCASTER Albion moved top of the NCE Premier as Josh Greening’s brace inspired a 3-1 triumph at Rainworth Miners Welfare while former leaders Worksop Town were felled 3-2 at Maltby Main.
Albion fell behind to a third-minute penalty converted by Matthew Sykes but Greening levelled just four minutes later and the Brewers led at half-time after Adam Baker’s goal nine minutes before the break.
Victory, and top spot, was sealed by Greening’s second strike one minute after the hour.
Bridlington Town moved second after thumping visiting Brigg Town 7-1 with braces from Chris Adams and Joel Sutton plus strikes from Will Waudby, Jamie Reeson and an own goal.
Albion are well-placed with games in hand on the two teams below them.
Thackley were denied victory at Handsworth Parramore whose Richard Adams struck at the death as part of a 3-3 draw. A Thomas Dugdale double and Joe Brown strike had Thackley 3-2 up.
Pickering Town, though, overcome visiting Parkgate 3-2 with strikes from Mitchell Hamilton, Joe Danby and Ryan Cooper.
A late Andrew Davis strike was in vain for Nostell Miners Welfare who lost 2-1 at home to Staveley Miners Welfare while Garforth Town lost 1-0 at Albion Sports. Pontefract Collieries were defeated 2-0 at Barton Town Old Boys.
In Division One, leaders Hemsworth Miners Welfare took a giant stop towards sealing the title with a 1-0 win at second-placed AFC Mansfield. A Harry Viggars strike ten minutes from time put Hemsworth 11 points clear, and with a game in hand.
Ashley Flynn slammed in a four-timer for fifth-placed AFC Emley who saw off visiting Westella VIP 6-3. Kieran Ryan and Jordan Corduri also netted for the hosts.
Elsewhere, Knaresborough Town enjoyed a 3-0 win at home to Grimsby Borough as Fraser Lancaster, Fatlum Ibrahimi and Ben Parkes all struck.
Selby Town won by the same score at Glasshoughton Welfare thanks to a brace from Will Ramsey plus a Danny Bunch penalty.
Eccleshill United, though, were undone by a Lewis Poucher brace in a 2-0 loss to visiting Hull United.