Teenager Leroy Lita, starting a league game for the first time, headed City to a narrow win which confirmed them in second place in Nationwide Division Two.
Scoring is no problem for Lita, released by Chelsea, as he has scored four times after coming off the bench.
This was a vital strike though as City came under second-half pressure from a determined Rushden side giving everything for new player-manager Barry Hunter.
For Hunter it was an eventful night with an injury, a header against his own bar and a booking for sweeping Lita to the ground as the 19 year-old rounded him.
Lita's chance to start came as manager Danny Wilson made three changes in a bid to pump up his scoring power.
City ran up a sequence of four corners as early as the second minute, but Rushden might have gone in front a minute later as Paul Underwood shaped to volley in a chip from six yards.
A desperate challenge from Christian Roberts saw him send the shot high over the top.
With his touch-and-run style, Gary Mills orchestrated some stylish raids for Rushden and Rodney Jack was always on the look-out for an enterprising run. But there was no finishing power to their attacks.
City's game was drifting the same way with Matt Hill, on his return from injury, badly over-hitting passes in the rain.
But it all fell into place for them when Louis Carey emerged from defence with a strong run on the right and a deep cross.
As Aaron Brown headed it back Lita spring-heeled for his decisive header, leaving Hunter injured and in need of treatment.
An excellent goal was tarnished for Lita though, when the youngster was booked for taking a dive as Hunter went in with the challenge.
Lita's all-action approach almost brought him a second goal as he intercepted a back-pass from Andy Edwards, but with the keeper racing off his line he rolled the ball wide.
The lack of a second goal nagged away at City as Rushden's confidence put them on top for a long spell in the second half.
The closest they came to an equaliser saw Jack, fed by Mills, get his shot on the right past home keeper Steve Phillips only for it to find the foot of the far post.