On-loan Manchester City forward Guidetti, who scored his first Celtic goal in Wednesday's win over Hearts in the Scottish League Cup, benefitted from a penalty-box scramble to break the deadlock three minutes before half-time on Saturday.
Kenny McLean levelled for the hosts early in the second period after Celtic goalkeeper Craig Gordon had denied Jason Naismith, but Guidetti beat Gordon's opposite number, Marian Kello, at his near post to move Ronny Delia's team to within five points of Dundee United with a game in hand.
Leaders United were 2-0 winners at home to St Johnstone after Chris Erskine gave them a 23rd-minute lead on the break.
Michael O'Halloran hit the post for St Johnstone but Paul Paton blasted into the top corner with 18 minutes to play, stretching the early season pacesetters' unbeaten run to six games.
Hamilton kept up their pursuit of Dundee United and lie only two points back after a 4-0 demolition of Lanarkshire neighbours Motherwell at Fir Park.
The visitors had needed penalties to see of their opponents in the League Cup during midweek but there was a gulf between the sides on this occasion.
Tony Andreu gave Hamilton a 34th-minute lead and midfield colleague Ali Crawford burst forward to double the advantage on the stroke of half-time.
Mikael Antoine-Curier made it 3-0 with a 63rd-minute penalty before Crawford notched his second from a tight angle in stoppage time.
Fellow high-flyers Inverness Caledonian Thistle lost ground in an error-strewn 3-2 loss at Aberdeen.
Josh Meekings headed Inverness into a 16th-minute lead but Adam Rooney capitalised on a weak back-header from Gary Warren to level matters and Shay Logan blasted Aberdeen into a 40th-minute lead.
Marley Watkins hauled the away side level five minutes after the break but another mistake, this time from Ross Draper, allowed Jonny Hayes to complete the scoring.
At the other end of the table, basement boys Ross County picked up their first points of the season with a last-gasp 2-1 win over Dundee.
Filip Kiss set up Michael Gardyne to break the deadlock from close range after 27 minutes but David Clarkson's first goal for Dundee meant it was all-square midway through the second-half.
But right at the end, substitute Darren Maatsen smashed a shot into the roof of the net to delight the home faithful.
Elsewhere, Tope Obadeyi's brace either side of a Manuel Pascali header gave Kilmarnock a 3-0 victory over Partick Thistle.
