The world number 11 needed just over an hour and a half to see off Wozniacki 6-4 6-3 and claim her second title of 2017
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Federer’s victory sets up a re-match of January’s Melbourne Park title-decider against Spaniard Nadal, who earlier rolled over unseeded Italian Fabio Fognini 6-1 7-5
Konta broke Williams twice in the first set as she moved into a 3-0 lead, before the 36-year-old American salvaged one of those breaks
The 14-time Grand Slam champion earned a 6-2 6-3 triumph to set up a semi-final showdown against Fabio Fognini, who defeated Kei Nishikori to reach the final four
The fourth seed remains on course for another title triumph Stateside, less than a week on from becoming the oldest champion in Indian Wells history
It was a straight sets victory for Nadal
Djokovic’s decision follows that of world number one Andy Murray, who has also been forced to withdraw from the tournament with a similar problem
A lacklustre Murray lost to Canadian world number 129 Vasek Pospisil in the second round at Indian Wells last week