Town's generous defence gifted Leeds the opening goal after only four minutes as Joe Skarz and James Berrett left Luciano Becchio's cross to each other, enabling Robert Snodgrass to poke the ball home at the far post and justify his inclusion ahead of leading scorer Jermaine Beckford.
Snodgrass, full of running and ideas, gave Town's defence little rest but Skarz and Berrett recovered from their earlier blunder to make some vital challenges.
Andy Robinson had a headed goal disallowed for offside as Leeds enjoyed most of the first-half possession and Gary Roberts twice went close for Town who equalised within 30 seconds of the restart.
Leeds keeper Casper Ankergren failed to deal with Keigan Parker's cross and Skarz atoned for his earlier mistake with a close-in shot in the congested goalmouth.
Matt Glennon pulled off two point-blank saves to deny substitute Beckford and Becchio in rapid succession before Collins grabbed the glory for Town by turning home Danny Cadamarteri's cross.