O'Keefe, a rangy senior attack, generated four goals with two assists in Seneca's season opener.
Junior midfielder Matt Donnelly scored five goals and senior midfielder Mike Mannino added three for Clearview (1-1, 0-1 division).
Senior goalie Joe Dibabbo made 15 saves, several of the spectacular variety, for the Pioneers.
"Our guys showed tremendous heart," Clearview coach Rob Rieck said. "They showed the character of this club. They are going to fight. We just came up one goal short."
Both teams twice rallied from two-goal deficits in the entertaining game on a warm, windy afternoon on the Golden Eagles' grass field.
"Just a phenomenal game," Rieck said.
Clearview was in front, 10-8, after Mannino scored on a blast from the right side with 6 minutes, 35 seconds remaining in regulation.
But Seneca fought back as Kevin Gray scored his second goal on a dish from Nick LeSaint and Ryan Bradway scored his second goal on a feed from Gray.
The last minute of regulation was wild, as Dibabbo made a great save on a point-blank shot and Clearview's Collin Love hit the post at the other end with around 25 seconds remaining.
"I was happy with the way we fought back," Seneca coach Rob Davidson said. "We have some things we need to clean up, but our kids played hard."
About two minutes into the first four-minute overtime period, O'Keefe circled behind the net and fired a pass to Butler, who made a sharp cut on the left side of the cage.
Butler caught the ball and fired in one quick motion, sending the entire Seneca bench charging onto the field in celebration.
"It was a good pass and a great finish," O'Keefe said. "It's a great way to start the season, fighting back and getting the 'W.' "
Clearview 1 3 4 2 0 - 10
Seneca 2 3 1 4 1 - 11
Goals: C-Matt Donnelly 5, Mike Mannino 3, Tyler Richardson, Jackson Specht; S-Dan O'Keefe 4, Ryan Bradway 2, Kevin Gray 2, Nick LeSaint 2, Tyver Butler.
Saves: C-Joe Dibabbo 15; S-Tyler McCormick 6.
Seneca's Dan O'Keefe talks about the win.