Chris Wilder will be left to rue another occasion where his side more than matched their opponents but were beaten by a sucker punch.
As at Cambridge on Friday the visitors were given the lead by Ivan Toney, this time after just four minutes, and they held on until five minutes from time when Noble-Lazarus equalised for the League One side.
Rochdale then won the game in normal time as Lancashire headed home to end the Cobblers cup involvements for the year.
A busy spell of fixtures has brought little reward for Wilder and his men despite some good performances. They return to league action at the weekend at home to Stevenage.
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