Atanackovic scored two of his goals after halftime to turn a 1-0 Falcons lead into a comfortable advantage.
In the 46th minute, Atanackovic took a pass from Salar Hajimirsadeghi with his back to the goal, turned and fired a shot straight into the left corner from 35 yards out for a 2-0 lead.
Five minutes later, it was Hajimirsadeghi again taking a pass up the left sideline from Jaehoon Jung out of the corner and sending it into the box where a crashing Atanackovic was able to score on a header.
St. Francis didn't score until the 63rd minute, when some crisp passing in the attacking third set Mark Verso up with an easy goal.
"That was our best moment of the day," St. Francis Coach Glen Appels said. "Three good passes and a finish — we needed a little more of that.
"We had some rough patches, they played very well."
Neither team was able to assume control of the game until Atanackovic put the Falcons up, 1-0, with eight minute left in the first half.
Golden Knights goalkeeper Hector Carranza successfully deflected a 20-yard free kick by Atanackovic out of bounds, but on the ensuing Falcons corner kick, Jung set Atanackovic up with an easy tapper in the goal box.
"The first goal we were a little sloppy," Appels said. "We were slow seeing it coming and that put us behind, which is always difficult."
St. Francis had a few chances after Verso's goal, including shots on goal by Verso and Eric Bocanegra inside the final 11:00, but couldn't solve CV's defense right to the end.
"I'm definitely very happy, not only with the defense, but with our team effort," said Falcons Coach Kiel McClung, who got six saves from backup goalkeeper Nick Ruiz, who filled in for Stephan Eng (thumb injury). "Just their willingness to battle and get in there and make the big plays for us."