Wilson tapped home from close range after Andrew Surman's initial shot had bounced back off the post.
Bournemouth needed a stunning one-handed save by Artur Boruc from Jamie Mackie's volley to help seal a vital three points.
The Cherries have a one-point lead and superior goal difference at the top of the Championship with three games left.
Norwich stay second, although Watford can join them on 82 points if they beat Nottingham Forest on Wednesday.
Middlesbrough also have not given up the chase for automatic promotion, with their victory over Wolves moving them to 81 points.
The race for the top flight remains extraordinarily tight and although victory confirmed a place in the play-offs at the very least for Bournemouth, manager Eddie Howe's side have their sights set on the league title.
With one eye on Saturday's FA Cup game against Arsenal, Reading manager Steve Clarke could have been forgiven for fielding a weakened side. However, he made just one change to the team that drew with Blackburn at the weekend and his side gave the league leaders a stern test at the Madejski Stadium.
The Cherries, roared on by vociferous away support of over 4,000 fans, made a blistering start, though, stunning the home crowd after only four minutes.
Wilson side-footed home from the six-yard box after Surman's initial shot from 18 yards came back off the post.
Reading rallied and only a superb, point-blank save by Boruc from Mackie's close-range strike kept the Cherries in front.
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The Royals' Jordan Obita later blazed over from a promising position, while Bournemouth's Yann Kermorgant floated a header wide of Reading keeper Adam Federici's post.
Matt Ritchie came close to doubling the lead on the hour, his fierce curling strike from the corner of the penalty box fizzing just wide, and Steve Cook later stung Federici's palms.
The closing stages were scrappy and niggly but despite intense late pressure, which included five minutes of injury time, Boruc was not tested and Bournemouth held on, inching ever closer to their first elevation to top-flight status .
The Royals remain 18th, eight points above the relegation zone, with Clarke's men having four games left to play.
Reading assistant boss Kevin Keen told BBC Radio Berkshire:"For manager Steve Clarke we were just about the better team, but the best team in the league won.
"We deserved at least a draw, we were competitive, but sometimes football is like that
"Confidence can carry you at this time of the season and hopefully this time next year we'll have that confidence.
"If you give Bournemouth a goal head start it is very hard. Artur Boruc save was outstanding but that typifies a team at the top of the league. Like I said I thought we deserved a draw."
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