The striker netted his seventh goal of the tournament in the 52nd minute of Tuesday night's semi-final at Fir Park when he curled into the top corner from 25 yards.
Saints were the better side for the majority of the game and survived some late pressure to book their first League Cup final appearance since 1956.
Jim Jefferies had led Hearts to their last final appearance in the tournament but his side were lacking a cutting edge again, following his losing return to the manager's job at St Johnstone on Saturday.
Jefferies had Andrew Driver, Ian Black and Lee Wallace back in the starting line-up following injury but Gus MacPherson won the tactical battle after bringing Chris Innes into a three-man central defence.
Andy Dorman was also recalled as Saints looked to the midfielder to play off Mehmet and Michael Higdon on a poor surface.
The tactics looked sound in the first quarter with the Hearts defence stretched several times. Mehmet and Lee Mair had half-chances from crosses but neither header troubled Marian Kello.
Dorman then played the ball in front of Higdon inside the box but the Englishman could not get it out from his feet and Kello easily saved his weak effort.
The pitch was cutting up so badly that MacPherson went on to the pitch to replace divots during stoppages but his team continued to cope better than Hearts.
Ross won the ball on the edge of the box and saw his shot deflect inches wide off Marius Zaliukas, before Mehmet shot into the side-netting from 20 yards.
Hearts lost Ismael Bouzid to injury in the 25th minute with Dawid Kucharski coming on but the Edinburgh side soon settled.
However, their only chance of the first half came when Smith failed to turn Christian Nade's knockdown on target from close range.
St Mirren regained the initiative after the break and Kello almost gifted the opener when his poor goal kick went went straight to Higdon, but Zaliukas got back well to dispossess the striker inside the box.
The Paisley side complained when Black, who had been booked in first-half injury-time for persistent fouling, caught David Barron late without punishment but they were soon celebrating.
Ross rolled the ball inside to Mehmet, whose controlled shot evaded Kello's leap and found the top corner.
Black was substituted and replaced by Suso Santana but Hearts were almost finished off when Mehmet held the ball up after Saints defended a corner and found Dorman's bursting run.
The midfielder raced clear but Kello narrowed the angle and got down well to block his powerful low strike.
Hearts continued to look vulnerable but Steven Thomson produced two weak efforts on a promising break and Mehmet's attempt to repeat his goal fell foul of a bobble and his shot sailed over.
Mehmet took out two Hearts players with a brilliant piece of skill to set up Ross to cross but Hearts cleared the danger.
MacPherson was soon on the pitch again but this time to remonstrate with Barron after the full-back dallied in possession inside his box, with his fellow defenders coming to the rescue to block Santana's shot.
Hearts finally exerted some pressure but John Potter cleared Driver's low cross from his goalmouth and Nade could not turn the winger's cutback on target.
Mehmet and Nade were booked for an injury-time clash before the final whistle heralded the St Mirren celebrations.