Djokovic won his third Australian Open title overall last year, adding the 2012 title to wins in 2008 and 2011. He has 12,920 rankings points, well ahead of No. 2-ranked Roger Federer's total of 10,265.
Andy Murray on Sunday defended his Brisbane International title and kept his ranking-point total at 8,000, which is third best.
Rafael Nadal, who lost in the 2012 Australian Open final to Djokovic, will miss the 2013 edition due to illness. Nadal is ranked fourth with 6,600 points, 95 ahead of No. 5 David Ferrer but could slip in the rankings.
Tipsarevic and Gasquet joined Murray in winning tournaments during the weekend. Tipsarevic won the Aircel Chennai Open in India on Sunday and Gasquet picked up the Qatar Exxon Mobil Open title Saturday.
Ferrer, a two-time defending champion at the Heineken Open, is the only ATP Top 10 player in a tournament draw this week.