Tom Anderson put the hosts on their way with his early opener before Omar Bogle doubled the advantage with his second goal in four games just after the break.
Niall Ennis, who played on loan at the club last season, gave Rovers a scare but the hosts held on for a welcome win at the Keepmoat.
“It’s a good result for us, of course it is,” reflected Butler, who took over after Darren Moore jumped ship for Yorkshire neighbours Sheffield Wednesday last week.
“There were some really good performances out there for us.
“It got a little bit nervy after we conceded the goal, but we had chances to make it a bit more comfortable.
“I think performance-wise the players put in an incredible shift on and off the ball so I’m really pleased.”
Veteran James Coppinger marked his 600th league appearance for the club with an assist as Anderson headed home the opener in the seventh minute.
Bogle was superbly kept out by a smart save from Michael Cooper. And it was another Coppinger cross which unlocked the door for the second as Bogle nodded in from close range.
But Ennis pulled one back two minutes later when he stabbed Conor Grant’s cross beyond Louis Jones.
Joe Edwards and Ennis both missed great chances to escape with a point as Rovers held on.
Doncaster: Jones, Halliday, James, Anderson, Wright, Smith (Gomes, 87), Bostock (Robertson, 45), Richards (John, 87), Sims, Coppinger (Lokilo, 72), Bogle. Unused subs: Balcombe, Horton, Greaves.
Plymouth: Cooper, Watts, Aimson, Opoku, Edwards (Moore, 83), Mayor, Reeves (MacLeod, 73), Grant (Lewis, 73), Fornah (Camara, 73), Jephcott (Hardie, 83), Ennis. Unused subs: McCormick, Lolos.
Referee: D Bourne (Nottinghamshire).
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