The three points saw the Toffees leapfrog the Swans to climb to ninth in the Premier League table. David Moyes's men were disciplined and organised from start to finish as the home side tried to pass their way through Everton's defensive ranks.
Their resilience was rewarded in the second half when Baines struck with a trademark free kick that left Michel Vorm with no chance.
After missing a flurry of chances, Jelavic recovered to apply the finishing touch to a Marouane Fellaini cross.
Swansea dominated the opening exchanges as a tired looking Everton struggled to disrupt the home side's passing game.
Whenever the visitors did win possession they were quickly hunted down by the hosts, with Joe Allen's industry powering the midfield engine room.
However, for all their huff and puff, the Swans lacked bite. Danny Graham, Gylfi Sigurdsson and Allen all roamed menacingly, but failed to trouble Tim Howard.
Breathing defiance at the heart of the visitors' defence was Phil Jagielka. The centre back made a series of crucial interventions in the first half, keeping the ball from Graham lurking dangerously in the box.
Brendan Rodgers's team nearly ended the half with 10 men after Allen flew into a rash challenge on Phil Neville. He escaped with just a booking.
Everton came out after the interval energised and set about neutralising the home side's slick football with a high tempo pressing game.
Leon Osman set the tone when he charged down a clearance from Ashley Williams, creating a chance for Jelavic.
The Croatian striker wasted the opportunity, hooking the ball over the bar, much to the relief of Williams.
The guests continued to dominate the second period and Darron Gibson stung the hands of Vorm with a ferocious drive from distance.
As the players began to tire, the game opened up and more chances started to fall for both teams. Graham headed over with Howard stranded. Steven Pienaar shot wide from 20 yards.
Then, with an hour played, Baines produced a moment of brilliance. The left back won a free kick on the edge of the box and stepped up to inflict maximum punishment with a curling shot into the top right-hand corner.
Pienaar almost doubled his side's lead minutes later when he cut inside from the left and bent a shot inches wide of the post.
In a bid to rescue a point, Rodgers rung the changes, making a treble substitution and switching to a diamond formation, but it was Everton who continued to dictate the play and Jelavic struck to seal the three points.
The Croatian looked destined to finish the game without a goal as he squandered two golden opportunities, courtesy of Pienaar's guile, before he tucked the ball in from close range.
Felliani stepped away from his marker in the box and laid a pass into the path of Jelavic, who had the simple task of tapping in from close range.
Pienaar's craft forged two more goalscoring chances, both for substitute Denis Stracqualursi, but the Argentinian was denied from close range by Vorm on both occasions.