The Hoops maintained their advantage over Aberdeen at the summit after a Kris Commons penalty and Stefan Johansen’s strike saw them take the spoils in a Glasgow derby.
James Craigen was sent off on the stroke of half-time for the visitors for conceding the spot-kick after bringing down Stuart Armstrong in the box.
The home side made a bright start and came agonisingly close to scoring in the first minute when Stuart Armstrong’s cross to the near post found Virgil Van Dijk, who stuck out a leg and his effort struck the crossbar.
Conrad Balatoni then saved his side twice, first with a last-gasp challenge to thwart Johansen before the defender’s headed clearance denied Guidetti an open goal.
Alan Archibald’s side slowly came into the game and went close to a goal only for Craig Gordon to pull off a stunning save at full stretch to keep out Kallum Higginbotham’s volley.
At the other end, Commons tried his luck with a 25-yard driver that flew inches over the bar.
The talking point of the half came on the stroke of half-time when Armstrong was brought down in the box by Craigen, who was shown a straight red for the challenge.
And Commons stepped up and scored the spot-kick to break the deadlock.
Celtic dominated the second period with their man advantage and nearly doubled their lead when Commons’ low strike was pushed away by Scott Fox.
And they got a second goal on 63 minutes when Johansen stroked the ball in after a clever lay-off from Guidetti.
Ronny Deila’s side could have increased their advantage a few minutes later when substitute James Forrest was sent through on goal but Fox stuck out a boot to make a good save.
And they should have scored their third goal in the closing stages when Gary Mackay-Steven’s cross fell on a plate for substitute Leigh Griffiths but he failed to find the target from a few yards out.
The Jags could have set up a tense final few minutes but Gordon pulled off a stunning one-handed save to keep out Gary Fraser’s drive.
And Celtic held on to move a step closer to the title while Partick remain in ninth place.