Burnley won at home for the first time in 10 attempts thanks to a second-half strike from substitute Robbie Blake.
Blake's volley after 65 minutes secured Burnley's first home win since their 2-1 victory over Norwich on 23 October.
Plymouth lacked a cutting edge, with Lilian Nalis's second-minute header proving their most threatening attack.
Wade Elliott and Joey Gudjonsson went close for Burnley in a low-quality first half, but Blake's introduction gave the home side the necessary spark.
Burnley manager Owen Coyle:
"It's a monkey off the lads' backs and we've got to make sure we take that on and turn out some more victories at Turf Moor.
"The fans again were great and we're delighted to reward them for their loyalty and the support they've shown.
"We passed the ball well, put numerous crosses into the box and had chances."
Plymouth manager Paul Sturrock:
"It's been a very difficult week for everybody and it seems to have seeped onto the football pitch.
"There was a lack of passion and I'm very disappointed, especially with certain individual performances.
"Starting tomorrow we're going to do it Paul Sturrock's way. There'll be a lot of work on the training ground."
Burnley: Jensen, Alexander, Caldwell, Varga, Unsworth, James O'Connor, Gudjonsson (Spicer 90), Harley, Elliott, Gray, Jones (Blake 56).
Subs Not Used: Kiraly, Garreth O'Connor, Jordan.
Goals: Blake 66.
Plymouth: McCormick, Connolly, Seip, Sawyer, Hodges, Summerfield, Nalis (Folly 75), Abdou (Smith 84), Halmosi, Jutkiewicz (Fallon 75), Easter.
Subs Not Used: Larrieu, Moult.
Ref: Anthony Taylor (Greater Manchester).