Chris Maguire's first-half poacher's goal after Paul Gallacher had spilled Craig Bryson's modest shot looked to have continued Kilmarnock's superb recent form under new manager Jimmy Calderwood.
But Mehmet struck in the 82nd minute with a glorious volley from 14 yards out to give Gus MacPherson's side hope that they can kick-start their league campaign.
Kilmarnock at least preserved an unbeaten record which stretches back to January 23, a seven-game run which has seen the Ayrshire side move well clear of the bottom of the league after the disappointment of the last days of Jim Jefferies' eight-year reign.
But the point was of much greater significance to St Mirren, who have not won in the league since January 12 and had picked up just one point from a possible 18 before the game to leave them perilously close to Falkirk, surprise winners on Saturday, in the relegation zone.
It was just their 12th goal in 12 away SPL games this season and Mehmet's strike brought the Co-Operative Insurance Cup finlists - who have beaten Kilmarnock three times already this term - their first league draw on the road this campaign.
Calderwood made two changes to the side which defeated St Johnstone, key defender Manuel Pascali returning after a leg injury to replace Tim Clancy while Conor Sammon came in for Danny Invincibile in midfield.
MacPherson was without Jack Ross as a result of the knee injury he picked up against Rangers and he was replaced by Steven Robb in the only alteration to the team which suffered a Scottish Cup exit at Ibrox.
St Mirren betrayed their recent dismal run of form by knocking the ball about beautifully in the opening minute and from the corner their fine play produced, the visitors had a couple of solid strikes blocked by timely Kilmarnock challenges.
It took the home side until the ninth minute to create their first chance, Maguire breaking clear down the right and crossing towards Sammon, who failed to strike his shot cleanly first time and allowed the visiting defence to clear.
St Mirren could have taken the lead three minutes later when English striker Mehmet rose impressively above the Kilmarnock defence but failed to direct Andy Dorman's corner on target.
St Mirren were far more comfortable in the first quarter of the match and came close to capitalising on their superiority in the 27th minute when Michael Higdon met Dorman's free-kick with a powerful header which forced Cameron Bell to tip over his bar for a corner.
Nothing came of the subsequent set-piece but the men from Paisley were threatening the Kilmarnock goal again within a minute, Dorman cutting in from the left to fire a right-foot shot which Bell handled competently.
The Ayrshire side's keeper also had to be alert on the half-hour mark when he dived at the feet of Steven Thomson after the playmaker had surged through the home defence from the centre of midfield.
Then, typical of the differing fortunes currently being enjoyed by both clubs, Kilmarnock took the lead in the 32nd minute against the run of play when Maguire, on loan from Aberdeen, scrambled the ball home from three yards out after Gallacher spilled Bryson's shot across goal.
Maguire, who also scored in last week's win over St Johnstone, almost doubled his tally - and Kilmarnock's lead -10 minutes later when he collected a headed flick from Kevin Kyle and volleyed just wide of Gallacher's right-hand post.
Calderwood made a change at half-time, Simon Ford - who had ensured a poor half by his standards and was continually beaten in the air by Higdon - being replaced by Rob Kiernan.
While the young Irishman started solidly in defence, the substitution did nothing to alter the pattern of the game as the visitors continued to look sharper in attack.
Calderwood's men did mount a dangerous counter-attack on the hour mark though, Sammon's direct running opening the way for Kyle to shoot powerfully enough for Gallacher to be happy just to turn the ball away for a corner.
MacPherson made a double switch in the 64th minute when Graham Carey and Allan Johnston entered the fray at the expense of Robb and Hugh Murray.
Maguire should have scored his second of the afternoon three minutes later when he sidefooted Sammon's inviting cross just wide of the right-hand post.
Perhaps sensing a late charge from the visitors, Calderwood took off striker Sammon and replaced him with defender Clancy with 20 minutes remaining, Jamie Hamill moving forward to midfield to accommodate the substitute at right-back.
St Mirren continued to press for the equaliser and Higdon volleyed just wide on 72 with Bell motionless in the Kilmarnock goal.
Kilmarnock were beginning to assert some authority in midfield but Calderwood decided to make another switch, Jamie Adams replacing Hamill with nine minutes remaining.
St Mirren then got the equaliser their play had warranted when Mehmet superbly volleyed into the left-hand corner of the net in the 82nd minute after Kilmarnock failed to clear their lines on several occasions.
Both sides pushed for a late winner but neither side could carve out a clear-cut chance as the game ended in deadlock.