Diamonds attacked Lincoln at every opportunity and looked anything like a struggling team. They controlled the second half, but finished up with just a point after having two goals disallowed for offside.
Lincoln, unbeaten since the start of the year, went close after just 55 seconds when McCombe set up Francis Green but the striker shot wide from five yards. Then Gary Birch tried his luck with a dipping shot from 25 yards which just cleared the bar.
But Lincoln's plans were thrown into disarray in the 21st minute when Northern Ireland international defender Gareth McAuley limped off with a hernia injury. As a result Nat Brown was brought into the back four with substitute Lee Beevers moving into midfield.
City went in front two minutes later when Rushden keeper Scott Tynan sent a clearance straight to Simon Yeo. The keeper found himself stranded on the edge of his box and was left helpless as Yeo coolly lobbed his shot into the empty net.
Another mistake by Tynan almost gifted Lincoln a second goal in the 41st minute. Green broke down the left and sent in a shot from a narrow angle which the keeper appeared to have covered. But he let the ball go under his body only to recover and save on the line.
Yeo missed another good chance for Lincoln, but the second half belonged to Rushden.
Skipper Wayne Hatswell shot wide from a good position before Simeon Jackson side-footed home only to see his 77th minute effort ruled out for offside. Three minutes later John Turner also found the net but was again ruled out by the assistant referee's flag.
Rushden finally drew level in the 82nd minute when Turner ran at the Lincoln defence and finished with a low shot into the bottom corner.
Two minutes later Lincoln were caught out by a long ball over the top and Jackson ran on to fire home.
But Lincoln were not quite beaten and in the third minute of time added on substitute Lee Frecklington pumped across into the box. The Rushden defence left McCombe unchallenged and the Lincoln central defender powerfully headed past Tynan to the relief of the home fans.