Morton had looked the more likely side to score, with Lawrence Shankland driving an effort off the bar before Andy Murdoch hit the post.
Vaughan latched on to a Ross McCrorie pass and applied a neat finish after the break.
Scott Tiffoney became the third Morton player to hit the woodwork late on.
The defeat means Morton, who have gone three games without a win, slip to third in the table due to Falkirk's win over Raith Rovers.
It was the second goal of the season for Vaughan, ironically on loan from Raith Rovers, and gave his side their first win against Morton this season.
More importantly, it provides a vital points cushion ahead of a big match with bottom side St Mirren in Paisley next Saturday.
The first half did not produce too manic chances, with Shankland hitting the underside of the bar from eight yards.
Sons defender Gregor Buchanan had a header from a 40th-minute corner headed off the line.
However, after the break, Morton came out fighting and Andy Murdoch rattled the post with a 20-yard effort that had Alan Martin beaten in the home goal.
However, on the hour mark, Vaughan produced the winner with a fierce strike past Derek Gaston in the Morton goal after a terrific driving run from Andy Stirling.
Morton's Scott Tiffoney then hit the bar with a cross-cum-shot before Sam Stanton's 70th-minute shot needed a terrific save from Gaston to keep the visitors in the game.
Shankland then had a 76th-minute effort chalked off by referee John Beaton for a push on Buchanan as the Sons held on to complete what could be a vital victory.
Dumbarton manager Steven Aitken: "That was a good battling performance and, when it comes to six games to go, it is not going to be pretty, but that is a vital three points.
"They had to defend for their lives for the last 20 minutes.
"However it is now a mini-league of four with ourselves, Raith Rovers, Ayr United and St. Mirren, so if we could win that league, it would be one hell of an achievement.
"They are big, big five games now and if we could get ourselves another three of four points then that might just be enough."
Greenock Morton manager Jim Duffy: "First half, we did not play well, but after the break, we did much better.
"We hit the bar twice, hit the post and. while I don't think we did enough to win the game, I think a point would have been a fair result.
"The players really worked hard and tried their best - maybe they were a bit heavy legged.
"We don't have the resources to change too many players, we tried to get a bit of energy and fresh legs, but it just was not to be on the day.
"Dumbarton do their job well and make it difficult for every team who plays here."
Match ends, Dumbarton 1, Morton 0.
Second Half ends, Dumbarton 1, Morton 0.
Attempt missed. Ross Forbes (Morton) left footed shot from outside the box is too high.
Attempt missed. Thomas O'Ware (Morton) right footed shot from the centre of the box is close, but misses to the right.
Foul by Andy Murdoch (Morton).
Calum Gallagher (Dumbarton) wins a free kick in the defensive half.
Corner,  Morton. Conceded by Daniel Harvie.
Attempt blocked. Ricki Lamie (Morton) header from the centre of the box is blocked.
Corner,  Morton. Conceded by David Smith.
Ross Forbes (Morton) wins a free kick in the defensive half.
Foul by Robert Thomson (Dumbarton).
Substitution, Dumbarton. Mark Docherty replaces Andy Stirling.
Substitution, Dumbarton. Calum Gallagher replaces Samuel Stanton.
Attempt missed. Lawrence Shankland (Morton) header from the centre of the box is just a bit too high following a corner.
Corner,  Morton. Conceded by David Smith.
Andy Murdoch (Morton) wins a free kick in the defensive half.
Foul by Ross McCrorie (Dumbarton).
Attempt missed. Thomas O'Ware (Morton) header from the centre of the box is close, but misses the top left corner following a corner.
Attempt blocked. Ross Forbes (Morton) right footed shot from the left side of the box is blocked.
Corner,  Morton. Conceded by Darren Barr.
Substitution, Dumbarton. Joe Nuttall replaces Lewis Vaughan.
Substitution, Morton. Gary Oliver replaces Luke Donnelly.
Attempt missed. Andy Stirling (Dumbarton) right footed shot from outside the box is just a bit too high.
Ross Forbes (Morton) wins a free kick on the right wing.
Foul by Daniel Harvie (Dumbarton).
Foul by Lawrence Shankland (Morton).
Daniel Harvie (Dumbarton) wins a free kick in the attacking half.
Derek Gaston (Morton) wins a free kick in the attacking half.
Foul by Robert Thomson (Dumbarton).
Attempt saved. Andy Stirling (Dumbarton) left footed shot from the left side of the box is saved in the bottom right corner.
Corner,  Morton. Conceded by Daniel Harvie.
Attempt saved. Samuel Stanton (Dumbarton) left footed shot from the left side of the box is saved in the bottom right corner.
Attempt missed. Ross Forbes (Morton) left footed shot from outside the box is close, but misses to the left from a direct free kick.
Ross Forbes (Morton) wins a free kick in the defensive half.
Foul by Stuart Carswell (Dumbarton).
Substitution, Morton. Aidan Nesbitt replaces Scott Tiffoney.
Substitution, Morton. Ross Forbes replaces Michael Tidser.
Attempt missed. Michael Tidser (Morton) left footed shot from the centre of the box misses to the right.
Scott Tiffoney (Morton) hits the left post with a right footed shot from the right side of the box.
Attempt blocked. Luke Donnelly (Morton) right footed shot from outside the box is blocked.
Lewis Vaughan's second-half goal was enough to give Dumbarton the points and move Steven Aitken's side above Raith Rovers into seventh place.