Paterson struck late in the first half and Hearts held on for a 2-1 victory after Jordon Forster had pulled a goal back in the 69th minute with a header of his own.
Hibernian's sixth consecutive defeat was sealed with a glaring late miss by substitute James Collins.
It leaves Hibs just a point ahead of Kilmarnock with three games left to avoid an 11th-placed finish in the Premiership and a relegation play-off against a Championship side.
Killie have lost three on the trot and only two points separate five teams but Hibs need to arrest an alarming slump or they will earn an unwanted extension to their season.
Terry Butcher's side have won just one game, against Ross County, since their New Year derby triumph, and have only opened the scoring once in 15 matches.
Butcher has struggled to find his best team throughout their awful start to 2014 and he made four changes, which included a surprise comeback for holding midfielder Scott Robertson after several months out with a knee injury.
That allowed Sam Stanton to play further forward off lone striker Jason Cummings, who came in as forwards Danny Haynes and Collins were dropped as Hibs aimed to improve on a goalscoring record that had seen them net just once in six matches.
The hosts made a nervous start but they gradually forced play forward, although there were almost 20 minutes on the clock when Hibs threatened first, Cummings glancing a header just beyond the far post following Liam Craig's cross.
Craig's return ball was inches from playing in Stanton as Hibs countered and Cummings forced the first save when he drove from 30 yards, Jamie MacDonald scrambling to his left to hold at the second attempt.
But the visitors took a 37th-minute lead with their first effort on target. Billy King earned a corner with some direct running down the left and he delivered a deep cross which Paterson won and headed down and saw it bounce through a crowded goalmouth and into the net past Craig on the post.
Paterson repeated the feat after Hearts were awarded a soft free-kick on the right wing after Ryan McGivern and Kevin Thomson challenged Sam Nicholson.
Kevin McHattie whipped the free-kick to the far post and Paterson attacked it and sent a header into the bottom corner.
Craig sent a tame free-kick straight at MacDonald moments later before the half-time whistle sparked resounding boos around the three home stands.
Forster, who was marking Paterson at both goals, almost got a goal back just after the restart with a header of his own following Craig's corner but his effort was cleared from the goalmouth.
MacDonald pushed wide long-range efforts from Thomson and Craig and Forster did begin to redress the balance when he raced in to meet McGivern's cross and head home from six yards.
Hibernian were handed a lifeline in the 84th minute when Craig charged down McHattie's clearance but Collins, their £200,000 summer buy from Swindon, miskicked as the ball flashed in front of him on the edge of the six-yard box.
Ryan Stevenson had a chance to put the game out of sight just before six minutes of stoppage time began when he was played clean through but he was just off-target after dinking the ball over goalkeeper Ben Williams.
Hibs' misery was completed with the final kick of the ball when MacDonald produced a stunning one-handed stop from Collins' powerful volley from the edge of the box, but the offside flag was up anyway and the final whistle went seconds later.