Everton defender Seamus Coleman was adjudged to have handled the ball and Shelvey tucked the resulting spot kick into the bottom corner in the 69th minute.
Aaron Lennon put Everton ahead with a close-range finish in the 41st after James McCarthy's cross from the left.Everton was heading toward the relegation zone a month ago but is now unbeaten in four matches.
Swansea, which lost striker Bafetimbi Gomis to injury in the first half, equaled its record points tally in the Premier League of 47.
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