The Finland international, who has joined on a season-long loan from Ukrainian club Metalist Kharkiv and looks a real coup for manager Mixu Paatelainen, scored after 56 minutes to claim all three SPL points for his new club on Saturday.
Kilmarnock had dominated the opening half and should have led by more than James Dayton's 29th-minute strike.
St Mirren levelled through Steven Thomson soon after the restart, but were unable to come back a second time as they were reduced to 10 men with Paul McGowan's sending off.
The on-loan Celtic forward was red carded for an apparent off-the-ball altercation with Manuel Pascali sparked by McGowan's failure to kick the ball out with Dayton, who had to be withdrawn, down injured in the opposite half.
St Mirren restored Thomson to their midfield, but were short of options in attack with Craig Dargo (knee) and Michael Higdon (groin) both missing through injury.
Kilmarnock offered the first threat, Conor Sammon's cross setting David Silva up at the far post, but his effort was comfortably gathered by Paul Gallacher in the St Mirren goal.
Silva then turned provider in the home team's next attack, his ball infield setting up a shooting chance for Craig Bryson, but his long-range attempt swerved wide of the mark.
Gallacher was forced into a fine stop in the seventh minute when Silva this time chose to go it alone and his powerful strike from distance needed pushing away for a corner.
Eremenko was impressing with his early touches and Gallacher needed to be alert again to keep out a direct free kick arrowed goalwards by the newcomer.
Kilmarnock were by now deserving of a lead, but a goal was proving elusive and from Dayton's corner, Momo Sissoko's far-post header looped agonisingly over the crossbar.
St Mirren managed a rare foray upfield after 24 minutes, Mark McAusland producing a fine low cross from the right, but Thomson's flicked header was always going wide.
Kilmarnock finally went ahead in the 29th minute, courtesy of a brilliant individual strike from Dayton, the winger cutting inside on the right before unleashing a fierce angled drive.
Dayton's joy was obvious and he darted the width of the field to embrace his manager, Paatelainen, who relaunched the midfielder's career this summer.
After his release from Crystal Palace in May 2009, Dayton struggled to find another club and spent last winter at Glenn Hoddle's football academy.
Kilmarnock should have doubled their advantage when another clever Eremenko pass set up an easy header for Silva, but he nodded over the crossbar from close range.
It was to be Silva's last contribution as he limped off in the 38th minute to be replaced by Harry Forrester, on loan at Kilmarnock from Aston Villa, who shot wide with his first touch.
Paul McGowan had the first attempt of the second half only seconds after the restart, but his attempt to surprise Cammy Bell dropped over the crossbar.
The visitors delivered after 48 minutes when Wardlaw's knock-on played Thomson in on goal and he thumped it in from close range with Kilmarnock protests at a possible handball in the move ignored.
Kilmarnock restored their lead in the 56th minute when Eremenko's free-kick caught out Gallacher at his near post and the St Mirren goalkeeper could only fumble it into the net.
St Mirren withdrew Thomson, who seemingly picked up a knock scoring his goal, on the hour mark and introduced another midfielder, Sean Lynch.
Gallacher redeemed himself a little with a fine stop after 62 minutes, beating away Sammon's shot after the Kilmarnock striker had been well set-up by Bryson.
There was controversy in the 63rd minute when McGowan was sent off for an apparent off-the-ball altercation with Pascali.
The incident was sparked by Kilmarnock anger at McGowan's failure to kick the ball out of play with Dayton down injured in the other half of the field after a collision with Jure Travner.
Forrester was also making an impact and he came close to making it 3-1 to Kilmarnock with a run and shot that fizzed just over the crossbar in the 78th minute.
Sissoko was next to burst from forward from defence and his 25-yard shot had Gallacher beaten only bounce the wrong side of the post, while the St Mirren goalkeeper made a superb one-handed stop to deny Forrester.