The away side made the perfect start when Chris Assombalonga was found in the area from a cross and the brother of Nottingham Forest striker Britt made no mistake, with his powerful header going in.
Guiseley attempted to get a hold on the game with Adam Smith firing just wide from 30 yards out, but it was the Daggers who showed their quality in possession with Fejiri Okenabirhie placing a shot just past the crossbar.
Dagenham started the second half as they finished the first as Okenabirhie had two chances in the opening minute.
His opening effort was a low drive that was saved by Atkinson and his next offering was a curled attempt from just inside the penalty area, which just went wide.
Dagenham, though, ensured they would get the three points, after Oliver Hawkins scored after being given a free header from a corner.
The hosts nearly halved the defecit late on, when substitute Adam Boyes fired a shot across the face of the goal.
Manager Mark Bower said “I’m disappointed with the performance and we deserved to lose this one. We didn’t have many players who stood out and hopefully this is a one-off.”
The second-bottom Lions are back in action tomorrow evening at third-bottom North Ferrriby United who are also winless after losing 2-0 at Dover on Saturday.
In National League North, a 90th-minute Damien Reeves header denied Harrogate Town all three points as Town and Altrincham played out an entertaining 2-2 draw at The CNG Stadium.
James Lawrie gave the recently-relegated visitors a tenth-minute lead, only for Luke Shiels to fire home his second goal of the season 14 minutes later to level. Town had led for the majority of the second half after Simon Ainge’s 54th-minute header, but were pegged back as stoppage time approached through Reeves’ flick.
Town now sit fourth ahead of tomorrow’s trip to bottom club Gainsborough Trinity.
Bradford Park Avenue, meanwhile, were also denied by late drama in a 1-1 draw at home to Nuneaton. Chris Sharp gave Avenue a 38th-minute lead but Joe Ironside bagged the visitors a point with his equalsier in the last minute.
Avenue are now sixth ahead of Tuesday’s trip to 16th-placed Chorley.
Recently relegated FC Halifax Town sit top of the division after a comfortable 3-0 win at home to Worcester City.
Halifax are back in action on Tuesday at third-placed Stockport.
Tadcaster Albion’s new adventure in the Evo-Stik League began in defeat as the Brewers were downed 2-0 at Hyde United.
Last season’s NCE League champions fell behind in the sixth-minute to a Philip Dean effort and the home side’s lead was doubled four minutes after the break through Christopher Amadi. Brighouse Town got off to the perfect start with a 2-0 success at home to Radcliffe Borough. The hosts were handed a dream opening when Reece Lyndon conceded a second-minute own goal and Radcliffe were put out of sight by Luke Parkin’s 71st-minute penalty.
Farsley Celtic also began with a bang through a 1-0 triumph at home to Colwyn Bay. Aiden Savory bagged the only goal of the game five minutes after the hour.
Ossett Albion showed fighting qualities to salvage a 2-2 draw at home to Clitheroe who led 2-0 after 62 minutes.
Goals from Kurt Willoughby and Dimitri Tuanzebe had the visitors in control but Ben Walker hit back in the 69th minute and Connor Brunt then salvaged Albion a point with his leveller five minutes from time.
Ossett Town will be keen to quickly move on from the opening weekend after a 2-0 setback at Prescot Cables. The hosts led after 27 minutes through a Robert Doran penalty and then doubled their lead 15 minutes from time through James Edgar.
Relegated Goole AFC also endured a miserable first day through a 3-1 loss at Ramsbottom United while Scarborough Athletic had to settle for a goaless draw at home to Bamber Bridge.
In the Premier Division, Frickley Athletic were given false hope in a 3-1 loss at home to Ashton United. The Blues led after six minutes through Tyler Williams but Ashton came roaring back through a Lee Gaskell double and Daniel Wilkins strike.
Whitby Town were denied by a late leveller in a 1-1 draw at Sutton Coldfield Town.
Hemsworth Miners Welfare made it two wins out of two in the NCE Premier with a no-nonsense 3-0 defeat of visiting Garforth Town.
Nash Connolly fired Hemsworth in front after two minutes before Del Pollock made it 2-0 eight minutes later. Hemsworth were then 3-0 up by the 20th minute after Connolly added his second, with Town now top on goal difference.
AFC Mansfield also have six points after Lynton Karkach bagged a last-minute winner in a 2-1 triumph at Harrogate Railway who led through Stephen Bromley.
Thackley followed their opening day triumph with a 2-1 loss at Cleethorpes Town whose Marc Cooper hit an 88th-minute winner. Thackley led after 12 minutes through Daniel Broadbent but Luke Mascall levelled two minutes after the break.
Liveresdge made it four points out of a possible six by steam-rollering visiting Armthorpe Welfare 5-0. Vaughan Redford, Rhys Davies, Joe Walton, Tom Jackson and Stephen Wales all bagged a goal each.
Eccleshill United have six points out of a possible six in Division One after edging a 3-2 success at home to Grimsby Borough. An Adam Turner strike and Luke Harrop brace saw Eccleshill to all three points.
New boys Campion top the division on goal difference after their 3-0 win at Selby Town.
Knaresborough Town bagged their first point in a 2-2 draw with visiting Worsbrough Bridge Athletic whose Matthew Pinder levelled with the last touch of the game. Goals from William Lenehan and Tom Woolard had Knaresborough heading for victory.
Pontefract Collieries bagged their first win with a 2-1 verdict at Ollerton Town thanks to Michael Dunn’s second-half brace while Yorkshire Amateur also obliged 3-1 at Shirebrook Town thanks to goals from Curtis Bernard, Joel Hughes and Carl Heard.
Glasshoughton Welfare also got up and running by ousting visiting Rossington Main 3-2 as Nathan Keightley, Adam Walsh and Adam Hayton netted one each.
But a Stephen Smith strike was in vain for Nostell Miners Welfare who lost 2-1 at home to Penistone Church.