Lubomir Michalik headed home a late winner at Elland Road to give Leeds' Coca-Cola Championship survival push added momentum.
The big Slovakian international's 87th-minute effort was his first goal for the West Yorkshire club and lifted them out of the bottom three for the first time since November.
It was rough on Plymouth, who had by far the better chances in the second period, but Leeds are now unbeaten in their last five matches.
David Healy raised the roof at Elland Road for the second week running with a late first-half equaliser after Peter Halmosi had given Plymouth a 35th-minute lead.
Halmosi silenced an expectant crowd by holding his nerve when racing onto Sylvan Ebanks-Blake's throughball, but Leeds went in level with Healy side-footing home his seventh goal in his last four matches.
Leeds manager Dennis Wise made no changes to his starting line-up after his side turned in their best display of the season last week when beating Preston.
But Ian Holloway made five changes after Plymouth followed up a 3-0 defeat at Ipswich with a 4-0 midweek trouncing at Burnley, with David Norris, Sylvan Ebanks-Blake, Peter Halmosi, Gary Sawyer and Bojan Djordjic all returning to the starting line-up.
Robbie Blake fired in Leeds' first effort on goal after wriggling clear inside the area, but Plymouth goalkeeper Luke McCormick comfortably gathered his left-foot shot, while Halmosi was wayward with two early long-range shots.
David Healy's low right-footed free-kick was a yard wide of McCormick's left-hand post, while another effort from the Irishman flew over the crossbar.
Plymouth defender Paul Connolly then denied Leeds a certain opener, the right-back getting a toe to Jonathan Douglas's cross before Richard Cresswell at the far post.
But Leeds goalkeeper Casper Ankergren had to be alert at the other end when Bojan Djordjic's 25-yard shot arrowed towards the bottom corner.
Halmosi's assured finish soon after was too good for the Dane though. Ebanks-Blake's trickery left two Leeds defenders flat-footed before the former Manchester United trainee clipped a fine ball into the Hungarian's path.
Halmosi outpaced a struggling Frazer Richardson, who limped off and was replaced by Alan Thompson soon after, and slid the ball underneath Ankergren.
But Leeds equalised just before the interval with Healy reacting quickest when Cresswell lost control in the area to shoot home from close range.
Thompson's 30-yard free-kick after a marauding Eddie Lewis had been upended was comfortably held by McCormick before Healy almost fired Leeds into the lead.
The little striker raced onto Gray's 40-yard pass over the top and steered the ball inches wide with the outside of his boot.
Plymouth then gave warning that they were still in the hunt for all three points when Norris let fly with a dipping 25-yard drive that was brilliantly turned away by Ankergren.
The Leeds goalkeeper then pushed away substitute Scott Sinclair's long-range effort in similar fashion and tipped Halmosi's cross-cum-shot over the crossbar.
But Leeds maintained their recent habit of scoring crucial late goals.
Thompson delivered a top-class free-kick following a shove on Lewis and Michalik headed back across goal and in off the post to the relief of most of the 30,034 crowd.
Teams:
Leeds Ankergren, Richardson (Thompson 39), Michalik, Heath,Gray (Rui Marques 80), Blake (Moore 65), Kishishev, Douglas,Lewis, Healy, Cresswell.
Subs Not Used: Stack, Johnson.
Booked: Gray.
Goals: Healy 45, Michalik 87.
Plymouth McCormick, Connolly, Timar, Seip, Sawyer,Djordjic (Sinclair 74), Norris, Nalis, Halmosi,Ebanks-Blake (Fallon 86), Hayles.
Subs Not Used: Buzsaky, Capaldi, Gosling.
Booked: Timar.
Goals: Halmosi 36.
Att: 30,034
Ref: S Mathieson (Cheshire).