Tom Anderson put the hosts on the right track with his opening 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, scared the Rovers, but the hosts held on for a welcome win at the Keepmoat.
“It’s a good result for us, of course,” said Butler, who took over after Darren Moore left the ship for Yorkshire neighbors Sheffield on Wednesday last week.
“There were very good performances for us.
“It got a little nervous after conceding the goal, but we had opportunities to make things a little more comfortable.
“I think performance wise the players made an incredible change on and off the ball so I’m really happy.”
Veteran James Coppinger marked his 600th league appearance for the club with an assist as Anderson led the opener in the seventh minute.
Bogle was superbly sidelined by a clever save from Michael Cooper. And it was another Coppinger cross that unlocked the door for the second as Bogle nodded at close range.
But Ennis fell back two minutes later when he stabbed Conor Grant’s cross past Louis Jones.
Joe Edwards and Ennis both missed great opportunities 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 Submarines: 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 Submarines: McCormick, Lolos.
Referee: D Bourne (Nottinghamshire).
Support the Yorkshire Post and become a subscriber today. Your subscription will help us continue to bring quality information to Yorkshires. In return, you’ll see fewer ads on the site, get free access to our app, and receive exclusive member-only offers. Click on HERE register.