The Sky Blues went behind just after the half-hour mark when Newcastle's Jobe Wheelhouse scored at EnergyAustralia Stadium but managed to equalise right on the stroke of half-time through John Aloisi before Stuart Musialik and Chris Payne both netted in the second half, delighting Lavicka.
"I want to mention the character of this team. We played well as a team and individually today," Lavicka said.
"After last week we wanted to show our fans that we can play and we did. We started actively and strong.
"We were punished with our one mistake but it was very important that we equalised before half time and then Stuey scored with an excellent strike and we get the three points. We are very happy.
"I want to say a big big thank you and how much we appreciate the Sydney FC fans and what they did here today. It was like a home game. They never stopped all game and it was very important to us."