Svensson is one of five players who are one shot behind Ben James at nine under par. The 23-year-old American leader is making his first professional appearance, having recently finished first in the PGA Tour's college rankings.
During the second round, Svensson had seven birdies and two bogeys, finishing at 65 strokes, five under par for the day.
Alex Norén fared worse, shooting 75 (+5) and missing the qualifying mark in his bid for next week's U.S. Open. Pontus Nyholm (+4) has also finished.
Jesper Svensson was also in second place at the start of his most recent tournament, in Texas in May. He finished ninth there.
