He replace Yasir Shah after returns of 7 for 83 in the second innings of the Antigua. Root moves up to No. 2 among batsmen
Josh Hazlewood and Nathan Lyon shared six wickets bowled out Sri Lanka for 117. Australia were 66-2 at stump.
England thrashed Pakistan by 330 runs in the second Test at Old Trafford to level the four-match series 1-1.
After a gap of four years since their previous tour in 2011, Australia are set to play three Tests on the Sri Lankan soil, starting Tuesday.
Zimbabwe strike bowler Tendai Chatara has been ruled out of the test series against New Zealand after hurting his ankle, Zimbabwe Cricket announced on Monday.
At stumps, England looking to level the four Test series at 1-1, were 98 for one with Alastair Cook 49* and Joe Root 23* in the middle.
Ashwin picked up seven wickets in the second innings as India defeated West Indies by an innings and 92 runs in first Test.
Mohammad Shami (4/66) and Umesh Yadav (4/41) helped India bundle out WI for 243, Following on, WI ended Day 3 at 21/1, trailing India by 302 runs.
Joe Root made his highest Test score of 254 and Chris Woakes took three wickets as England completely dominated Pakistan on day two at Old Trafford on Saturday.
It was memorable day for Virat Kohli, who eased to his maiden double hundred in Tests before R Ashwin (113 off 253) struck his third Test ton.