Albion, who now boast five successive clean sheets, survived a late rally from the Royals to record their first league win over the Berkshire side in 12 attempts.
The Seagulls have now won five of their last six home games and Reading's defeat still leaves them without a clean sheet away from home for six months.
Reading threatened early on when winger Hal Robson-Kanu shot just wide of keeper David Stockdale's right-hand post following a move involving Matej Vydra and Yann Kermorgant.
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Brighton's French winger Anthony Knockaert then fired into the side-netting after a surging run down the left by striker Sam Baldock.
Israeli international midfielder Beram Kayal, recalled by manager Chris Hughton in place of veteran Steve Sidwell, had a low free-kick saved after Danny Williams brought down Dale Stephens on the edge of the area.
Keeper Ali Al Habsi came to Reading's rescue shortly after by keeping out a low goal-bound shot from Stephens with his leg following good work by Sam Baldock.
Manchester United loanee Wilson, restored to the Albion attack in place of Tomer Hemed, failed to get sufficient contact on a teasing ball across the six-yard box by Baldock.
But England Under-21 international Wilson made no mistake to fire the hosts ahead on 25 minutes with a cool left-footed finish inside the keeper's left-hand post after Baldock's pace took him past skipper Paul McShane.

James Wilson celebrates with team mates after scoring the first goal for Brighton

Image credit: Reuters

Reading wasted an opportunity to get on level terms 10 minutes before the break when Albion keeper Stockdale could only parry a fierce shot from Vydra and midfielder Michael Hector wastefully blazed the rebound over the bar.
Wilson threatened to double the Seagulls' advantage when he headed over at the far post after Knockaert whipped in a free-kick with pace.
Reading keeper Al Habsi showed alertness to gather the ball under pressure from Baldock following a long throw by skipper Bruno Saltor.
The pace of strikers Baldock and Wilson continually gave Reading problems and the former was narrowly off target after the influential Knockaert delivered the perfect pass.
Albion should have increased their lead just after the hour mark when Baldock set up Scottish winger Jamie Murphy, but the former Sheffield United man put a shot wide as Al Habsi narrowed the angle.
Reading struggled to create many clear-cut opportunities, although Robson-Kanu forced Stockdale to make a save midway through the second half.
Dutch striker Ola John should have hit the target for Royals 13 minutes from time when he wastefully volleyed over from eight yards after a knock-back by Kermorgant but the hosts held on for maximum points.
Elsewhere, Hull's automatic promotion bid continued to falter as they were held to a second successive home draw and slipped to fourth in the table.
Hull were held 1-1 by Nottingham Forest, the same score as against MK Dons at the KC Stadium on Saturday.
Birthday boy Daryl Murphy scored his first goals for two months as Ipswich continued their push for a play-off place with a 2-0 victory over Blackburn.
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