Clayton Donaldson`s third goal in two games ensured that Crewe will take their place in the second round despite them being pushed all the way by Blue Square Premier side Ebbsfleet in a 1-0 win at Gresty Road.
The FA Trophy holders rose to the occasion and dominated from the off with Neil Barrett almost giving them a dream start when his overhead kick flew just wide of the post.
Mark Ricketts then nearly caught Steve Collis off his line with a free-kick as United grew in confidence.
Kezie Ibe also went close with a curling effort that forced Collis into a fine save before Donaldson struck in the 34th minute to grab an undeserved goal.
The former Hull man scored twice in defeat at Huddersfield a week ago, but spun his man on the edge of the box to power home and earn Alex the win.
Michael Gash wasted Ebbsfleet`s best chance after the break as he too went close with an overhead effort.
Football Results
Team Bath 0-1 Forest Green A Second-half goal from Kaid Mohamed was enough to send Forest Green in to the second round of the FA Cup following their 1-0 victory over dominan...
AFC Hornchurch 0-1 Peterborough Craig Mackail-Smith's late strike broke the hearts of Ryman Premier outfit AFC Hornchurch and ensured Peterborough marched on to the second round ...
Havant and W 1-3 Brentford Goals from Marvin Williams, Charlie MacDonald and Nathan Elder ensured Brentford avoided an FA Cup upset at the home of Blue Square South side Hav...
Carlisle 1-1 Grays Athletic Gary Madine saved Carlisle's blushes with an equaliser seven minutes from time to earn a 1-1 draw against Blue Square Premier strugglers Grays
AFC Telford 2-2 Southend Jon Adams` brace was enough to earn AFC Telford a deserved replay as Jean-Francois Christophe spared Southend's blushes in a 2-2 draw
Aldershot 1-1 Rotherham Aldershot striker John Grant showed nerves of steel to keep his team in the FA Cup as his 93rd-minute penalty earned a 1-1 draw with Rotherham
Bournemouth 1-0 Bristol Rovers Jason Pearce was the hero as he grabbed the winning goal as Bournemouth booked their place in the second-round with a 1-0 win over Bristol Rovers
Brighton 3-3 Hartlepool Tommy Fraser grabbed a late equaliser to earn Brighton an FA Cup first round replay in a thrilling 3-3 clash with Hartlepool
Cheltenham 2-2 Oldham Oldham earned a replay after coming back from two goals down at the break to earn a 2-2 draw at Cheltenham
Colchester 0-1 Leyton Orient Leyton Orient edged through to the second round of the FA Cup thanks to a 1-0 win at League One rivals Colchester