Virgil van Dijk's third goal in two games was enough to give Ronny Deila's side all three-points, and open up an advantage over Inverness Caledonian Thistle for the first time this season.
After dominating proceedings at Parkhead the hosts eventually got their breakthrough on the hour-mark, but they needed a superb late save from Craig Gordon to deny the visitors a point.
Aleksandar Tonev, Scott Brown and Van Dijk all saw first-half chances saved by Paul Gallacher, and the the Partick keeper was on hand again to deny John Guidetti on a number of occasions.
The Swedish striker saw a powerful header saved, before Anthony Stokes blazed wide from a Guidetti pass just before the break.
Patrick rarely threatened at the other end, with Gordon only called into action once to divert an Abdul Osman header wide.
Chances were not as frequent in the second half, but Deila's men eventually got the decisive goal thanks to Van Dijk.
The defender met a Stefan Johansen free-kick in the six-yard box and lashed the ball beyond Gallacher, having also scored twice against Hearts in the Scottish Cup at the weekend.
Substitutes Kris Commons and Stefan Scepovic went close to doubling Celtic's lead in the closing minutes, before Gordon produced a fine one-handed save to deny Kris Doolan.
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