Matias brilliantly lobbed the Owls into a 37th-minute lead but New Zealander Chris Wood equalised in the 61st minute with his second goal in as many games.
Leeds has drawn all four of its Championship games this season and should have made better use of its possession against a Wednesday side which rarely tested goalkeeper Marco Silvestri.
Leeds pair Kalvin Phillips and Gaetano Berardi were cautioned early on for clumsy tackles, the former receiving his yellow card inside 60 seconds as referee Michael Jones looked to impose his authority on a potentially explosive derby.
Leeds was quicker to settle, Stuart Dallas and Mirco Antenucci shooting close from distance and the latter being flagged offside after running on to Sam Byram's intelligent through ball.
Yet it was Wednesday which struck in the 37th minute. Vince Sasso's long high pass caught out the Leeds defence and Matias flicked the ball from right foot to left, wrong-footing Liam Cooper, as he sent an immaculately-judged lob just under the bar in a classic smash-and-grab raid.
Wednesday defender Tom Lees was booked against his old club for shirt-pulling and Leeds almost equalised just before the break when Antenucci's cross was chested just wide by Wood.
Despite abundant effort from both teams, it had been a largely untidy first half, with Mr Jones' whistle rarely far from his lips.
Leeds was quicker out of the traps at the start of the second half and, after Liam Palmer had hurriedly conceded a corner, Sol Bamba headed Phillips's flag-kick straight at keeper Lewis Price, who was again deputising for Kieren Westwood.
Phillips then rustled the side-netting with a free-kick awarded for a foul on Byram by Matias just outside the right corner of the penalty box.
Leeds made a double substitution in the 56th minute, Alex Mowatt and Luke Murphy replacing Byram and Phillips.
Mowatt's first contribution was to send a speculative shot high over the bar as Leeds struggled to break down the Owls' stubborn defence.
They were at last rewarded just after the hour mark when inspirational captain Bamba combined with Mowatt to send Dallas cutting in from the right and he rolled the ball into the goalmouth where Wood stretched to prod his second goal in as many games.
Both sides squandered gilt-edged chances within a minute. First Kieran Lee should have restored Wednesday's lead in the 67th minute but after a swift build-up he headed weakly at Silvestri. Then Wood had most of the goal to aim at but contrived to nod the ball wide from eight yards.
Ipswich Town stayed top with a 2-1 victory at Preston North End in which both of its recruits from AFC Bournemouth found the net.
Brett Pitman and Ryan Fraser were both part of the Cherries side that won promotion to the Premier League last term but now find themselves aiming to guide Ipswich to the same feat this time around.
Pitman - signed on a permanent deal in June - opened the scoring with a headed effort in the 24th minute, before Daniel Johnson made it 1-1 at the break.
However, on-loan Fraser clinched the win by curling home a superb 25-yard effort to leave Ipswich ahead of Brighton & Hove Albion - a 1-0 victor over Blackburn Rovers - on goal difference.
Johann Berg Gudmundsson struck deep into second-half stoppage-time to earn a 2-1 win for Charlton Athletic against Hull City.
A remarkable eight clubs remain winless after four fixtures, with Rotherham United bottom of the pile after a 4-2 defeat to Queens Park Rangers, and Bolton Wanderers having moved a point clear of the New York Stadium outfit with a 1-1 draw against Nottingham Forest.
Elsewhere, Burnley beat Brentford 1-0, Fulham drew 1-1 with Huddersfield Town and Reading was held to a goalless draw by Milton Keynes Dons, while Middlesbrough suffered its first defeat of the season at home to Bristol City.
In the day's late kick-off, Cardiff City picked up its maiden win of the campaign, beating Wolverhampton Wanderers 2-0.
