Leigh Griffiths' 14th goal of the season after nine minutes proved to be the difference between the two sides as Celtic failed to break down a resilient Hibs outfit.
Despite the loss, Neil Lennon's side are still six points clear at the top of the SPL ladder with a game in hand while Hibs are fourth, nine points behind the Glaswegians.
Meanwhile, Kilmarnock gave away a two-goal lead as they played out a 2-2 draw with Motherwell at Fir Park.
Borja Perez put the away side ahead on 13 minutes and Paul Heffernan doubled Killie's advantage just after the hour mark.
However, two goals in three minutes from Jamie Murphy and Henrik Ojamaa after 71 and 74 minutes respectively ensured Motherwall enjoyed a share of the spoils.
Niall McGinn scored a hat-trick as Aberdeen dispatched bottom side Dundee FC 3-1 at Dens Park.
All of McGinn's goals came in the second half with an 82nd-minute Mark Stewart goal representing the only highlight for a Dundee side whose winless run in the league now stretches to six matches.
St Johnstone and Inverness played out a 0-0 draw with the scheduled match between Ross County and Hearts postponed due to a waterlogged pitch.