Heroes of Telford United's run to the fifth round 25 years ago were presented to the crowd before kick-off. But the current Bucks' chances of matching the feat were dealt an early blow when Sergio Torres finished neatly into the bottom corner after Clarke had provided an excellent cross from the right flank.
The equaliser came four minutes after the interval when Blakeman threw himself at Jon Adams' right-wing cross and looped his diving header majestically into the top corner, but the Imps hit the front again after 65 minutes when the impressive Clarke drilled home a crisp, low drive from the edge of the box.
Luck completely deserted the Blue Square North side three minutes later when Carl Rodgers' thunderbolt volley from long-range cannoned off the crossbar - one of many second-half near misses.
Full-back Aaron Brown secured Lincoln's place in the second round 15 minutes from time when he rounded off an incisive breakaway by screaming home a left-foot shot from the edge of the box.