Celtic picked up a vital yet impressive three points at the Skuna Stadium with Celtic in control for most of the 90 minutes and could have extended their lead in both halves.
The winning goal saw Correia convert from the spot to net his seventh goal since joining the club.
Celtic started the game on the front foot and Tranmere loanee Jake Burton, making his second Celtic debut saw an early looping shot saved by Danny Taberner inside 60 seconds.
Shane Killock followed this chance up with a header from a Stephen Brogan free-kick but Killockâ€™s header was narrowly over the bar.
Dougie Nyaupembe and Sam McLintock both saw efforts fall wide of the target in a dominant opening 20 minutes from Celtic which should have seen a Celtic penalty on 21 minutes.
Correia beat Taberner to the ball inside the penalty area, Correia got to the ball first and touched it past Taberner who clattered into Celticâ€™s number nine but the referee decided that there was nothing wrong with that incident.
Seven minutes later and an almost repeat scenario took place, Correia capitalised on a poor clearance, he chased the ball down and Taberner collided with the striker with the referee this time pointing to the spot.
Correia stepped up and comfortably slotted the spot kick past Taberner who dived the wrong way.
Celtic continued with their first half dominance and went close to a second on two occasions before the break.
On 41 minutes, McLintock picked out Burton inside the penalty area with a low cross from the right, Burton turned but fired just over the bar.
Just two minutes later and Correia managed to win the ball back in Athertonâ€™s final third, from a tight angle his effort was just wide of the near post.
Celtic took a one goal lead into the break.
Athertonâ€™s only shot on target during the 90 minutes came immedaielty after the restart with defender Luca Defreitas Hansen heading straight at Grant Shenton from a free-kick.
Celtic Under 18â€™s graduate Matty Jones was introduced mid way during the second half for McLintock and Celtic had a great opportunity to double their lead on 68 minutes.
Sam Wedgbury played Burton in on goal, he raced forward and forced a good save from Taberner who tipped his goal bound effort over the crossbar.
Celtic saw the remaining minutes out well and the defence coped with Athertonâ€™s balls into the box with ease.
The final whistle came after four additional minutes with Celtic victorious and deservedly earning three big points.
Celtic: Shenton, Nyaupembe, Edwards, Wedgbury, Quansah, Killock, Burton, Doyle, Correia, Brogan, McLintock (Jones â€™65).
Subs not used: Leach, Ubah, Harris, Johnson.
Celtic are next in action on Tuesday with Whitby Town the visitors to Bower Fold.
|2||Sinclair, Sky||> 49|
|8||Lambert, Danny||> 31|
|10||Rokka, Elliot||> 54|
|12||Smith, Aaron||< 54|
|15||Gannon, Oli||< 31|
|17||Batts, Niall||< 49|