Smith, making his first start of the season in place of the injured Paul Gallacher, punched Liam Craig's corner into his own net in the 36th minute and spilled a shot to allow Francisco Sandaza to score just after the break.
Craig wrapped up the victory before the hour mark as St Johnstone closed the gap on third-placed Motherwell to five points.
Smith, who was replaced as first-choice goalkeeper despite helping the Pars to the First Division title, was one of four changes to the side that lost 4-0 to Hearts last weekend.
Paul Willis came into midfield and Paddy Boyle and Jason Thomson returned in defence but the Pars never looked like getting back in the game after the opener as they continue to await their first home win of the season.
St Johnstone came into the game on the back of three consecutive defeats, all at home, but their away form has been a different story.
Only Hibernian have beaten them on the road this season and they have now conceded only two goals in their other nine away games.
Saints also had three key players back in their team with captain Jody Morris and top goalscorer Sandaza returning from injury lay-offs and Callum Davidson back after illness ruled him out of last weekend's defeat by Celtic.
The Pars made a decent start in blustery conditions and it could easily have been St Johnstone goalkeeper Peter Enckelman who put his team in trouble.
The Finn raced well off his line as Andrew Barrowman ran on to a Paul Burns pass on the right wing when there appeared little immediate danger.
Enckelman was easily beaten to the ball but Barrowman could not take advantage of the open goal as he shot two yards wide from the touchline.
The wind was proving a challenge as both sides struggled to mount meaningful attacks and Willis sent a ball across the face of goal when his team-mates were calling for a cutback after the midfielder worked his way into the box from the right flank.
St Johnstone began to push their hosts back but they still could not carve a chance. Several Liam Craig deliveries did not fall for a team-mate and Smith got down to hold Sandaza's shot after the Spaniard had outmuscled Alex Keddie outside the box.
But St Johnstone were gifted a 36th-minute opener when Smith's first game of the season turned into a personal disaster.
The former St Mirren goalkeeper came off his line to punch Craig's inswinging corner from the right but the ball spun the wrong way off his fist and Willis could only help the ball into the roof of the net as he attempted to clear off the line.
Smith made a good save five minutes later when he stopped Craig's low, angled drive after the St Johnstone midfielder had turned a defender to put himself clear on goal.
And the grounded goalkeeper's luck turned as Sandaza hit the bar from 10 yards from the rebound.
Smith's day got even worse seven minutes after the break as he spilled a shot from Marcus Haber to allow Sandaza to double St Johnstone's lead.
Haber got reasonable power on his shot from the right channel after taking Murray Davidson's pass in his stride but Smith had got his body and two hands behind the ball and should have held.
Instead the ball spun out and Sandaza was the only man to react, getting in front of Thomson to slide home from close range.
Dunfermline were pushing more men forward but the game moved further out of sight in the 59th minute.
Sandaza beat Thomson to the ball 30 yards out to leave the home defence exposed and the Spaniard's disguised pass to Craig left the midfielder one on one with Smith.
This time the Dunfermline goalkeeper had no chance as Craig lifted the ball over him into the far corner.
Dunfermline brought on Ryan Thomson, Andy Kirk and Liam Buchanan but an attacking spark failed to materialise and St Johnstone saw the game out comfortably with Morris rested for the final 15 minutes.