Two years ago, the American's rant at a lineswoman over a foot-fault call earned her a point penalty that cost her defeat in her semi-final against Kim Clijsters on Arthur Ashe Stadium.
Williams missed last year's tournament with a foot injury that, coupled with related blood clots in her lungs, kept her out of the game for a year.
She returned a week before Wimbledon and, perhaps unsurprisingly, struggled through three rounds at the All England Club before losing to Marion Bartoli in the fourth.
Since then, though, the 29-year-old has returned to full match fitness and went into the tournament on the back of a 12-match winning streak that included titles in Stanford and Toronto. Jovanovski, 19, is considered one of the brighter talents in the game but she swiftly discovered the size of the challenge ahead as Williams smacked winners past her in the opening game.
The Serbian got on the board in the fourth game but Williams was making very few unforced errors, moving well and serving superbly, giving Jovanovski no chance to get into the match.
The American wrapped up the first set in 25 minutes and the second took only six minutes longer as she cruised through to a second-round meeting with Dutch qualifier Michaella Krajicek.
Williams comfortably maintained her record of never losing in the first round of a Grand Slam, but she admitted to nerves before she walked out on court.
The 28th seed said: "I always have little jitters I think before I play. You've just got to play through it. I was thinking, I'm just trying to hold the little record I have of first rounds.
"Eventually things are meant to be broken, but hopefully it won't happen soon."
Williams had burst into tears after winning her first-round match at Wimbledon against Aravane Rezai, but there was very little emotion from the 13-time grand slam champion on Wednesday.
Williams said: "Wimbledon was amazing for me to even be there and play. Here I have had more preparation and I've been doing better. Again, I'm happy to be here. But it was just a totally different thing."
The 29-year-old is the hot favourite to win the title, not that she is thinking about things that way.
She added: "I'm just here to play. Everyone's been playing all year and I haven't. I've played five tournaments this year. I don't think that's usually a favourite going into a grand slam.
"It is what it is. I can't even express how excited I am to be playing."