All-rounder Curran was named player of the tournament, and also scooped top honours for his performance in the final, after taking 13 wickets in six appearances in Australia while Rashid was outstanding in the knockout stages.
Rashid has moved up five spots to number three in the new update, with Curran in at a career-high of fifth place.
Wanindu Hasaranga of Sri Lanka, who topped the World Cup wicket charts with 15, remains in first place with Afghanistan's Rashid Khan next.
Alex Hales, who recently returned from a three-year international exile, and starred in the semi-final win over India with a match-winning 86 not out, is also on the up among batters.
He jumped 22 spots to number 12, nipping one place in front of captain and opening partner Jos Buttler.
Dawid Malan, who missed the business end of the tournament through injury, remains England's highest-ranked batter in sixth.
Suryakumar Yadav of India retains top spot ahead of Pakistani duo Mohammad Rizwan and Babar Azam.