Leeds, who earlier this season looked odds-on favourites for automatic promotion, have won only four of their 13 league games in 2010 and face the prospect of being dragged into the play-offs again, where they lost last year to Millwall.
Morison steered an early shot wide after breaking clear of Patrick Kisnorbo but made amends after 10 minutes when he steered in Liam Trotter's cross from the right at the far post.
Leeds took their time to get going but improved as the first half wore on and Jonny Howson had their best chance of the first period when he beat Jimmy Abdou but dragged a right-foot shot from the edge of the box wide in the 44th minute.
The east Londoners almost added a second in first-half stoppage time when Paul Robinson's header following a corner clipped the top of the crossbar, before Robert Snodgrass blasted over a good opportunity for Leeds 10 minutes into the second half.
Morison fired into the side-netting after a swift counter-attack in the 66th minute, and with 10 minutes to go substitute Batt made the result safe.
He evaded some weak challenges as he cut in the left before his low right-foot shot beat Leeds goalkeeper Casper Ankergren at the near post.
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