Lewis Grabban scored the only goal at Villa Park as Steve Bruce's team moved to within two points of the automatic promotion places and established an unassailable cushion over seventh-place Middlesbrough.
Grabban headed Villa into the lead in the 29th minute, directing a finely floated left-wing centre from Jack Grealish back across goal to beat Leeds goalkeeper Bailey Peacock-Farrell.
The visitors fought back after the interval but Paul Heckingbottom's men could not find a way to beat Villa keeper Sam Johnstone, who kept a clean sheet in a home win for the third time in succession.
Jedinak played the entire match and started at centre back where he's played a number of games for the club this season in the absence of John Terry.
The 33-year-old, who has been in and out of the Villa squad this season, won 10 of his 14 duels and ended with a passing accuracy of 63 percent as he edges closer to a Premier League return.