Molinari makes World top 20
The 29-year-old, who beat Darren Clarke by three shots at Loch Lomond, is ranked 19th going into the British Open where Tiger Woods will be defending his number one position.
Phil Mickelson will take over at the top of the rankings if he lifts the Claret Jug, but a top-four finish would be good enough for the Masters champion if Woods misses the cut for the second year running.