The Reds dug deep to level scores after conceding in the 10th minute of Saturday's match before Clough goaled in the second half and survived a VAR check for offside to nab the four points at Coopers Stadium.
Carl Veart's men could finish as high as third on the table this round, after two wins and one draw to start the A-League Men season.
Meanwhile, Western United (0-2-2) remain winless after coughing up an early lead and conceding an own goal.
Adelaide's Ryan Kitto had opened the door for the visitors to draw first blood when he fouled Riku Danzaki, giving away a free kick outside the box.
United centre-back Dylan Leonard's pass towards goal bounced between players before Kane Vidmar snuck it past the Adelaide defence to cap the set piece.
But their dominance did not last long.
With off-season recruit Dylan Pierias as the spark, Clough pulled off a cutback to teenager Luka Jovanovic.
Jovanovic sent the goal just wide but the ball deflected off 17-year-old Leonard into goal in the 32nd minute.
Vidmar cleared the ball but his desperate act was too late, with a VAR check confirming the Western United own goal.
Talk about a game of inches �😲 After VAR review, — Isuzu UTE A-League (@aleaguemen) @AdelaideUnited draw level by the finest of margins!Seriously unlucky for 17-year-old defender Dylan Leonard, but the Reds won't care!Watch #ADLvWUN live NOW on Paramount+ and 10 Bold 📺 pic.twitter.com/aXr0HmPVwlNovember 9, 2024
Englishman Clough had a chance to build a lead before half-time but his shot on goal lacked the power and made for an easy save for keeper Matthew Sutton.
Sutton immediately turned over possession but Reds attacker Stefan Mauk overshot his attempt after successfully dancing his way through opposition.
Clough finally hit the scoreboard in the 71st minute when he received a clever pass from Jonny Yull deep in the box.
Former Reds sharpshooter Hiroshi Ibusuki momentarily stole the show when he was greeted with an accidental punch to the face by keeper James Delianov.
Moving to Western United in the offseason, Ibusuki was looking to make a header when Delianov - who had eyes on the ball - charged forward to clear the threat with his fist.
Ibusuki, who was already sporting tape near his left eye, shook off concussion concerns and finished the match.
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