Button got his lucky break in the race when team-mate Rubens Barrichello, following close behind in second, and forming a barrier between Button and Raikkonen, suffered graining tyres 10 laps into the race.
However, she again pressed the self-destruct button rather than pushing forward, wasting a chance to break Jankovic before seeing her own serve falter again.
The 2003 campaign will be Button's fourth since he was given his grand prix break by Williams in 2000, though he is still looking for his first podium finish.