A deflected Adam Le Fondre effort was enough to dump the Imps out of the Johnstone's Paint Trophy at Don Valley Stadium on Tuesday evening.
In-form Le Fondre, who scored four on his last outing on home soil for the Millers, struck two minutes into the second half with his effort from the edge of the box hitting the unfortunate Moses Swaibu before beating a wrong-footed Joe Anyon between the sticks.
Prior to this blow, City had enjoyed the better of the opening period with skipper Scott Kerr coming close early on whilst Andy Hutchinson curled a 20-yard effort a foot over the bar.
Chances after the interval, however, were few and far between and in the end it was Le Fondre's 47th minute effort which sent the 87 travelling City fans home disappointed and booked his side a place in the second round of the competition.
MATCH FACTS
LINCOLN CITY
1 Joe ANYON
2 Paul GREEN
4 Adam WATTS
5 Moses SWAIBU
3 Joe ANDERSON
8 Clark KELTIE
11 Scott KERR
25 Cian HUGHTON
14 Josh O'KEEFE
22 Andy HUTCHINSON
27 Ben HUTCHINSON
subs
18 Delroy FACEY (for GREEN 40)
24 Nathan ADAMS (for KELTIE 76)
19 Jamie CLAPHAM
21 Sam TURNER
20 Paul MUSSELWHITE
BOOKING: SWAIBU (82)
ROTHERHAM UNITED
30 Jamie ANNERSON
17 Johnny MULLINS
5 Ryan CRESSWELL
22 Exodus GEOHAGHON
3 Tom NEWEY
7 Nicky LAW
8 Jason TAYLOR
4 Danny HARRISON
15 Kevin ELLISON
24 Jeremiah ANI
10 Adam LE FONDRE
subs
14 Luke ASHWORTH (for GEOHAGHON h/t)
16 Paul WARNE (for ANI 65)
12 Jamie GREEN (for LE FONDRE 86)
23 Dean HOLDEN
31 Danny HANCOCK
GOAL: LE FONDRE (47)
BOOKING: ASHWORTH (67)
MATCH OFFICIALS
REFEREE: David Coote
ASSISTANTS: Martin Coy & Scott Duncan
FOURTH OFFICIAL: Adrian Holmes
ATTENDANCE: 1,677 (87 City supporters)