Sela enjoyed a straight sets triumph over 21-year-old wild card Christopher Eubanks.
The Israeli described himself as “satisfied” with his performance in a 6-2, 6-4, 6-2 success.
Sela will face a tougher test against 17th seed Sam Querry as he looks to reach the third round for the first time.
29th seed Schwartzman of Argentina was equally impressive in dismissing the challenge of countryman Carlos Berlocq.
He ran out 6-2, 6-1, 6-3 victor to set up a clash against Janko Tipsarevic as he looks to reach the third round of the grand slam for the first time.
But there was disappointment in the Ladies Singles for Camila Giorgi of Italy. She went down 6-3, 6-4 against No. 31 seed Magdalena Rybarikova of Slovakia.
