Playing a 4-5-1 formation, Leeds took the lead with 2 minutes played when Lloyd Sam's cross found United captain Jonny Howson, who headed the ball in the back of the net.
United doubled their lead when loanee Sanchez Watt crossed the ball in for Luciano Becchio who volleyed and smashed it in the back of the net.
Soon after, Bradley Johnson, Sanchez Watt and Jonny Howson were close to scoring a third.
On half time, Sam did head the third Leeds goals in after a great chip by Paul Connolly. Lincoln to plan B and Leeds up to 3.
In the second half, Lincoln pushed hard to get a consolation goal. However it was Leeds who scored their fourth when after a couple of step overs, Sam was tripped for a Leeds penalty. Neil Kilkenny put the ball to the right of the goal past Joe Anyon to make it 4-0 to United.
The full time whistle blew and Leeds were into the next round of the Carling Cup.
Leeds United: Schmeichel, Connolly, Bruce, Collins, Bessone, Howson (Hughes 72), Kilkenny, Johnson (White 61), Watt, Becchio (Grella 61), Sam. Subs: Higgs, Naylor, Hughes, Bromby.
Lincoln: Anyon, Green, Swabu, Watts, Anderson (Clapham 46), Carayol, O'Keefe, Jarrett, Kerr (Hutchinson 72), Hughton, McCallum (Facey 62). Subs: Musselwhite, Keltie, Broughton, Clarke.
Referee: P Tierney Attendance: 12,602