Eastwood suffered their fourth straight defeat at home the first time this has happened since November 2014.
Basford made an excellent start, Nat Watson heading in from Courey Grantham's precise cross after just two minutes play.
Basford keeper Saul Deeney made a superb save from John Whitehurst's shot, but otherwise it was Basford in control, the team playing some good possession football and taking the sting out of the home side's efforts.
Half hour in, a good flowing move ended with Zak Goodson's pass being fired home from ten yards by Watson to double the lead.
Three minutes into the second period, Courey Grantham made it 3-0 from close range after Stef Galinski's shot had been blocked on the line following a corner.
That effectively ended the game as a contest, with Basford in control without ever really threatening.
Basford keeper Deeney was a virtual spectator until the final minute, when he got down well to save from Pat Webb's free kick.
Eastwood CFC: Jake Pearson, Kallum Greaves, Sam Meakin, Reuben Mitchell, Billy Brooks (c), Danny Hayes, Rory Smith, John Whitehurst, Joe Butler (Louis Czerwak 55), Jack Allen (Chay Bettridge 64), Patrick Webb.
Subs Not Used: Jack James, Jack Walker, Kieran Knight
Basford: Saul Deeney, Jack Thomas, Louis Tomlinson, Jerry Nash, Liam Bateman, Stef Galinski (Levar Gayle 77), Fernando Bell-Toxtle, James Reid, Nat Watson (Dan Creaney 63), Courey Grantham (Joe Wroughton 83), Zak Goodson.
Subs not used: Shaun Harrad, Kieran Preston.
Attendance: 108