The race was held in rainy weather at Sao Paulo.
Webber took the lead ahead of pole-winner Rubens Barrichello (Brawn GP Mercedes), a Sao Paulo native, after the first round of pit stops, and then easily beat Poland's Robert Kubica (BMW Sauber) and England's Lewis Hamilton (McLaren Mercedes), last season's F1 champion.
Button steadily went through the field to finish fifth and built an insurmountable 15-point lead over Sebastian Vettel, He is 17 ahead of Barrichello, who suffered a punctured left-front tire and finished eighth.
"Twenty-one years ago, I jumped into a car and I loved winning," Button said. "I never expected to be world champion."
Webber won his second F1 race, while Ross Brawn won the season's constructors' title.