Ea Lla Koto went into the encounter under immense after failing to replicate the same form which saw them win the Nedbank Cup last season, but Celtic never came to the party, making it almost easy for the home side to claim all three points.
As a result, Luc Eymael's side moved into the top eight for the first time this season, but despite the win, they still find themselves behind Phunya Sele Sele on the log.
Both teams had a slow start to the first half, but it was Celtic who looked comfortable on the ball although they couldn't turn that into clear-cut goalscoring chances.
Linda Bhengu and Tchilimbou tested the Celtic defence early on, but they were unable to penetrate the Stars defence which was marshalled by Rooi Mahamutsa.
Celtic, who went into the encounter with four wins, two draws and a single defeat, had a chance to break the deadlock 18 minutes into the game, bt Tshegofatso Mabasa couldn't beat goalkeeper Badra Sangare from close range.
The home side had a penalty shout turned down soon afterwards after Goodman Dlamini was brought down by Lorenzo Gordinho inside the box.
Komphela's charges took control of the game after the half-hour mark, but Ndumiso Mabena failed to test Sangare as the former's free-kick attempt went wide.
Stars broke the deadlock after 38 minutes when the Celtic defence was found in sixes and sevens to allow Tchilimbou to outjump them and head the ball past Tignyemb from a cross on the right hand side.
It was Stars in front at the interval, but Celtic came back guns blazing after the restart with Tebogo Potsane, formerly of Free State Stars, causing all sorts of problems in midfield.
Menzi Masuku and Gordinho missed two glorious opportunities inside the first 10 minutes of the second; perhaps goalscoring chances which may have changed the complexion of the game.
Jantjie then doubled Ea Lla Koto's lead with a stunning lob after realising that Tignyemb was off his line.
At this stage, there was no way back for the visiting team, and this didn't sit well with Komphela, who masterminded a goalless draw against Mamelodi Sundowns in midweek.
Their fans had expected Celtic to replicate last season's performance when they defeated Stars 3-0 in the local derby.
Jantjie was at it again minutes later as he forced Tignyemb to a low save midway through the second half as Stars looked to make it 3-0.
Playing in front of their home, Stars looked alive and they used their small pitch to stiffle Celtic, who looked too relaxed even they had the ball.
Mpho Maruping was unlucky not hit the back of the net with less than 15 minutes to go as his shot came off the woodwork with Tignyemb well beaten.
At this stage, Komphela knew that he wasn't going to win the match, let alone salvage a draw, and he will be disappointed with his team's attitude towards Free State Stars.
Ultimately, it was Stars who ran 2-0 winners at the expense of Celtic to move up to seventh on the PSL log.