Neither side did enough to take all three points in a dour contest but the Cobblers will have been happy to pick up only their fifth point of a frustrating campaign.
Northampton made a bright start and Ivan Toney went close several times on his full debut.
The young striker was twice off target with headers and also shot wide before he failed to turn home Chris Hackett's cross-shot.
In between, Padraig Armond fired wide for Morecambe on the counter attack.
Morecambe also made a better start after the break and twice went close to breaking the deadlock.
Former Cobbler Mark Hughes had his header hacked off the line by Darren Carter and Duke turned over the follow-up from Ellison.
At the other end, Toney was inches away from converting Roy O'Donovan's low cross but Northampton failed to seriously mount a challenge in the second half of a largely forgettable affair.
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