Goals from John Marquis, Mallik Wilks, James Coppinger and Matty Blair saw Rovers come from behind to secure victory.
Manager Grant McCann said: “I said to them at half-time that it would be a statement win and we’ve done that.”
After an even first half in which Marquis’s penalty cancelled out Walsall’s opener from Morgan Ferrier, Rovers dominated.
McCann continued: “In the second half we took it to another level. The character in the group is really good.
“We came to a club that hadn’t lost, with a new manager, a new identity, a team that works hard. I was speaking to Dean Keates (manager) before the game and he says the group just buys into hard work. We knew we had to match that if not better it if we were going to win.”
Former Saddlers captain Andy Butler gifted his old team the opener as his mistimed header set up Ferrier to nod home.
Doncaster levelled on the half-hour as Leahy handled and Marquis tucked home his fourth league goal of the season from the resultant penalty.
Goalkeeper Marko Marosi foiled Ferrier’s six-yard strike after the break before Rovers went in front as Leeds loanee Mallik Wilks drilled past Liam Roberts.
Wilks’s surging run set up James Coppinger to curl home a fine third before Matty Blair sealed the rout in stoppage time.
Walsall: Liam Roberts, Devlin, Fitzwater, Guthrie, Leahy, Morris (Ismail 72), Dobson, Osbourne (Ronan 53), Ginnelly (Gordon 80), Ferrier, Cook. Unused substitutes: Johnson, Dunn, Kinsella, Wilson.
Doncaster Rovers: Marosi, Mason, Wright, Butler, Andrew, Blair, Whiteman, Kane (Jermaine Anderson 75), Wilks (Taylor 84), Marquis, Coppinger (May 74). Unused substitutes: Lawlor, Beestin, Amos, Tom Anderson.
Referee: A Coggins (Oxfordshire).