The in-form striker took his tally to four goals for the season in the Spanish top flight with a clinical finish after 90 minutes at Estadio Manuel Martinez Valero, which earned Eduardo Berizzo's side their first away win of the campaign.
Nolito's strike moved unbeaten Celta up to fourth place in the table and stunned Elche, who had their chances during a disappointing encounter in which the home side came closest when visiting defender Andreu Fontas headed against his own crossbar.
Celta had drawn twice away from home already this season and Pablo Hernandez set about attempting to secure their first three points on the road when he tried his luck just three minutes in, but was off target.
The visitors lost Augusto Fernandez to injury just 26 minutes in, with Michael Krohn-Dehli replacing him, then Elche goalkeeper Manu Herrera had to be alert to keep out a strike from Fabian Orellana.
Elche responded and Jonathas fired just wide early in the second half, while Fontas had a stroke of luck when his header came back off his own bar.
Jonathas and Víctor Rodriguez then spurned chances to put the hosts in front 15 minutes from time and they were made to pay when Celta snatched victory with a goal out of the blue.
Krohn-Dehli was the architect, biding his time before cleverly dinking the ball over the top of the Elche defence for Nolito, who was allowed too much time to fire home the winner.
