Wrexham face a trip to Workington in the last 16 of the FA Trophy after a comfortable win at the Camrose.
Steve Evans' long ball led to the opener, a mix-up in the home defence seeing Adam Aimable divert the ball past Ross Kitteridge for an own goal.
Basingstoke rallied, but were killed off when Andy Fleming freed Sam Williamson, his pass finding Jefferson Louis who had a simple finish.
Sido Jambarti got a late consolation for Basingstoke from a free kick.
606: DEBATEThe match had been postponed twice due to the freezing conditions over the weekend.
The knock-on effect is that Wrexham's Blue Square Premier game with Torquay has been put back from Thursday to Friday (16 January).
Wrexham manager Dean Saunders:
"We just looked a bit rusty, we've been training on astroturf and it showed.
"Our passing wasn't as crisp as normal, nor was some of our movement or speed of thought.
"They had chances to score that I wasn't pleased about... we got the result, that's the main thing."
Basingstoke: Kitteridge, Aimable, Watkins, Williamson, Dolan, Maledon, Jombarti, Hateley, Bossman, Tait, Warner.
Subs Not Used: Tarpey, Ogunbote, Mitchell-Coop, Ruggles, Waller.
Goals: Jombarti 87.
Wrexham: Ward, Williamson, Louis, Taylor, Mike Williams, Evans, Fleming, Woolfe, Fairhurst, Flynn, Jonathan Brown.
Subs Not Used: Suffo, Kearney, Aiston, Spann, Spender.
Goals: Aimable 14 og, Louis 57.
Att: 597
Ref: M Thompson (England).
RELATED INTERNET LINKS:
Wrexham fans' views on 606
BBC Local: North East Wales
Wrexham weather
BBC Sport Non League
FA: The FA Trophy
Football Association of Wales
Wrexham AFC
Basingstoke Town
The BBC is not responsible for the content of external internet sites
~RS~q~RS~~RS~z~RS~26~RS~)