The reigning A-League champions, who are struggling down the wrong end of the table this season, produced a much-improved performance to net twice in the first half before surviving some scary moments late as the Jets pressed for an equaliser.
But it was the early part of the match which pleased Lavicka who now wants his side to push on for the remainder of the season.
"The difference today was we started the game very well and we played the first half actively," Sydney Lavicka said after the match."We put the opposition under pressure, we created a few chances and scored two goals.
"I think our current situation is not optimal of course but I have to give full credit for the Sydney FC players tonight because they showed character on the pitch. It's only a small step ahead for us but it's an important step."