Although Basford were far from overawed by the surroundings, they were soon put under pressure with Rob Smith having an early effort charged down, Matt Bowles being denied by a back-tracking defender and three corners being cleared.
The deadlock was eventually broken in the 20th minute when Alex Simmons got on the end of a Kegan Everington centre before planting a firm effort past Josh Downie in the Basford goal.
The lead should have been doubled shortly after the restart when Matt Cotton got the better of his marker only to prod past the advancing Downie, who then denied Smith with a fine save.
Nick Green doubled the scoring six minutes before the interval when he rose high to connect with a deep Simmons corner and the defender did well, diverting his header into the top corner.
Three minutes later Basford pulled one back when hesitation in the Imps' defence following a long ball over the top gave Henoc Isamene the chance to capitalise and this he duly did, rounding Henry Smith before rolling the ball into an empty net.
The last kick of the opening period saw centre-back Callum Ward denied by Downie with the centre-back finding himself in the attacking area whilst the Imps restored their two-goal advantage just 30 seconds after the restart thanks to a clinical finish form Simmons after he was released by Smith.
A fine fine header from Bowles made it 3-1 three minutes later before Simmons completed his hat-trick from the spot after Cotton was upended by Macauley Barber in the box.
Simmons was denied a fourth in the 57th minute when Downie sprinted off his line to block his low effort before Cotton drove over after cutting in from the left.
City's 12th corner of the game led to goal number six with substitute Jordan Harper picked put Bowles who volleyed through a crowd of players for his second of the tie, the ball taking a slight deflection before beating Downie.
Another substitute, Cenk Akar, set up Helsdown who was denied by the feet of Downie and he played a part in the Imps' seventh and final goal, linking up with Bowles who found Harper who finished powerfully from 12 yards in the 87th minute.
LINCOLN CITY U18
1 Henry SMITH
2 Nick GREEN
3 Kieran WALKER
4 Kegan EVERINGTON
5 Callum WARD
6 Jordon COOKE
7 Alex SIMMONS
8 Matt BOWLES
9 Kieran HELSDOWN
10 Matt COTTON
11 Rob SMITH
12 Mason LOVE (for WALKER 60)
13 Richard WALTON
14 Jordan HARPER (for SIMMONS 68)
15 Andy WRIGHT
16 Cenk AKAR (for COTTON 77)
GOALS: SIMMONS (20, 36 & 49), GREEN (39), BOWLES (48 & 72), HARPER (87)
BASFORD UNITED U18
1 Josh DOWNIE
2 Damian CHARLTON
3 Corey WRIGHT
4 Mohammed IDRIS
5 Macauley BARBER
6 Aaron COYLE
7 Henoc ISAMENE
8 Joe COXON
9 Dillon TIDESWELL
10 Umar ISMAEL
11 Joshua LEE
12 Reece PUNTER (for ISMAEL 60)
14 Jak LIGHTLY (for TIDESWELL 66)
15 Cole MITCHELL (for COYLE 78)
16 Steven DENNIS
17 Jack SWEET
GOAL: ISAMENE (42)
REFEREE: Duncan Robertson
ASSISTANTS: Jack Forder & Jerzy Banasik