The 19-year-old produced two instinctive strikes - one in each half - to see off a Kilmarnock side that never managed a shot on target over the 90 minutes.
Shunsuke Nakamura produced a fabulous finish with six minutes left to round off a comfortable night for the league leaders, as they moved four points clear at the top.
Celtic started well and Shaun Maloney tested Alan Combe early on but the goalkeeper was well positioned to save.
Maloney then shot wide when he should have done better after Sheridan had knocked down Nakamura's cross.
Andreas Hinkel then tried his luck with a left-foot shot from outside the box but his effort flew a couple of yards wide.
Celtic crafted the opening goal after 18 minutes. Sheridan headed on a long clearance to Scott McDonald and then took the return ball to beat Combe with a cool finish with his left foot.
The home side were getting things pretty much their own way but too often their final pass was not accurate enough to create a clear-cut chance.
Nakamura tried his luck with a free-kick which beat the wall but Combe managed to get across his goal to make a comfortable save.
Maloney then had a decent attempt with a free-kick from a similar distance but whipped the ball narrowly wide.
But there was a scare for Celtic after some slack defending in the 33rd minute when Mehdi Taouil was just inches away with a 20-yard shot with Mark Brown exposed.
Hinkel then made a good blocking challenge on Gavin Skelton as Kilmarnock showed they could pose a threat on the break.
McDonald had a great chance two minutes into the second half when he pounced on a throughball from Gary Caldwell but Combe managed to divert his shot for a corner.
Nakamura then came close with an 18-yard shot after good work by Hinkel had given him the chance.
Celtic needed the second goal to ease their concerns but they struggled to put the Kilmarnock defence under any sustained pressure.
It finally came 15 minutes from time when Combe failed to hold a shot from Massimo Donati and the ball broke for Sheridan to slam the ball into the roof of the net.
Nakamura completed the scoring six minutes from time when he beat Combe with a shot high into the net from inside the box.