Starting the day eight under par and one stroke behind Molinari, Westwood began in ideal fashion with a birdie at the first that the Italian matched.
Molinari then bogeyed the fourth to drop into a share of the lead with his English opponent but quickly rectified his mistake with another birdie at the fifth.
Both players then picked up another shot at the eighth as they continued to match each other over the outward nine, Molinari moving to 11 under par and Westwood one stroke behind.
The pair had started to pull away from the rest of the field with Ross Fisher, Luke Donald, Richie Ramsay and Jaco van Zyl leading the chase on seven under.
Fisher was two under for his round through 10 while Donald reached the turn one under on the day following a birdie at the sixth. Ramsay and Van Zyl were level par for their third rounds.
Charl Schwartzel and Pablo Martin were tied on six under while Padraig Harrington was six off the lead a shot further back, tied with Ernie Els and Noh Seung-yul in ninth.
Tiger Woods, meanwhile, had fallen back to three under par as three bogeys on his outward nine hindered the former World Number One.