Opening batsman Dimuth Karunaratne is the stand-in captain of a 17-man squad for the two-test series starting on Feb. 13.
Richardson, who only came into the side after Josh Hazlewood was ruled out with injury, had figures of 3-26 to lead an impressive Australian display with the ball.
The spotlight in Galle remains on the departing Herath, the most successful left-arm spinner in history, as he seeks a fairytale swansong.
While Sri Lanka took their catches and were brilliant with their ground fielding, the visitors were sloppy during the home team's innings.
Dickwella put on 137 runs with opening partner Sadeera Samarawickrama, who made 54, to give the hosts a perfect platform for their formidable total after electing to bat first.
The hosts, who trail 3-0 in a series badly affected by the Sri Lankan monsoons, after the opener was washed out, have made two changes in their bid for a consolation win.
Jos Buttler said the World Cup was in the back of everyone's mind, but they were taking every series one at a time and hoped to build a core group of players for next year's championship.
The world's number one ranked 50-over side, England are favourites despite a historically poor record on the island.
Mathews was earlier asked to step down from ODI captaincy after the Islanders crashed out of the Asia Cup following heavy defeats to Bangladesh and Afghanistan.
The sacking followed Sri Lanka's drubbing in the Asia Cup, with losses to lower-ranked Afghanistan and Bangladesh ensuring its quick exit from the competition.
Sri Lanka have been grappling with a leadership crisis over the last 18 months, during which Tharanga, Malinga, Kapugedera and Thisara Perera have also been tried as ODI captains.
The 28-year-old had sustained a finger injury during a match in the recently-concluded Sri Lanka Cricket T20 League 2018.
Chandimal, Hathurusingha and Gurusinha were banned for two Tests and four one-day internationals for violating the spirit of the game.
Sri Lanka were reeling on 75/7 in their second innings when bad light forced the umpires to bring the curtains down on the match.
India made no changes in the team, while Sri Lanka made two changes, bringing in Lahiru Thirimanne and Dinesh Chandimal.