In qualifying for his third Amateur in the last four years, Osberg, 28, of Philadelphia, posted rounds of 67 in the morning at Applebrook Golf Club in Malvern and 70 in the afternoon at Waynesborough, in Paoli, for a 5-under-par 137.
Six players survived the stifling heat and a delay of about an hour and a half for lightning in the area, and punched their tickets to the Amateur.
Osberg said he was "a little bit on the rocks" after the double bogey at the third hole, a score that began with a hooked tee shot into the trees.
"I made a good double," he said. "I wasn't discouraged, but I knew I had to play tight coming in. Then obviously, to hole out on the next hole and get it right back, I knew I was pretty much in control at that point in time."
Earlier in the day, Osberg holed out another lengthy shot, draining a wedge from 141 yards for an eagle 2 at the 12th hole at Applebrook.
Brandon Dalinka of Newtown, a former Council Rock North star and sophomore-to-be at North Carolina, and recent Villanova graduate Brian Colbert, the 2012 Philadelphia Amateur champion, both shot a 69 at each site and tied for second at 138.
Dalinka was coming off top-eight finishes at the New Jersey State Amateur and the New Jersey Open.
"I'm much more confident than I've ever been before," he said. "Last summer and the summers before that, I've been coming to these things trying to maybe have one round under par. But now, I've done it, I'm used to it. It's not uncomfortable to be under par."
Another Atlantic Coast Conference player, Virginia's Cory Siegfried, who graduated from the Haverford School and lives in Villanova, shot an afternoon 68 at Applebrook for a 140 total. The other two qualifiers were La Salle junior-to-be Michael Johnson, a Hatboro-Horsham graduate, and Cameron Liebert, a Malvern Prep product who will be a junior at Loyola (Md.).
Contact Joe Juliano at 215-854-4494 or email@example.com or follow him on Twitter @joejulesinq.
(Applebrook score listed first)
Jeff Osberg, Philadelphia . . . 67-70-137
Brandon Dalinka, Newtown . . . 69-69-138
Brian Colbert, Bryn Mawr . . . 69-69-138
Cory Siegfried, Villanova . . . 68-72-140
Michael Johnson, Ambler . . . 73-68-141
Cameron Liebert, Malvern . . . 69-73-142