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After last week's dismal defeat at Sheffield Wednesday, Blackwell warned his side against a repeat performance and it worked a treat.
The Championship side raced down the notorious Millmoor slope from the start and came close to an early opener.
Only a last-ditch challenge from Northern Ireland defender Colin Murdock halted Rob Hulse as he sized up an early shot.
And Rotherham were saved by the post when former Wednesday striker Cresswell saw his downward header bounce over keeper Neil Cutler but hit the upright before being cleared by Gregor Robertson.
But Cresswell struck in the 19th minute with an emphatic finish to give Leeds the lead when he smashed in a shot past Murdock on the line after the ball broke to him when Cutler dived to block Hulse.
Leeds were in no mood to allow Rotherham back in. Robertson curled a free-kick over and Martin Butler might have done better but fired wide as the home side found chances hard to come by.
Michael Keane curled a long-range shot wide after the break but Leeds were in cruise mode.
The visitors might have stretched their advantage but Cutler held onto a shot on the turn from Hulse.
Icelandic midfielder Gylfi Einarsson saw a shot saved and Cutler held onto another effort from Ian Moore.
Leeds boss Kevin Blackwell said afterwards: "We came up against a side who are doing quite well in the League and I think we did a thoroughly professional job.
"I'm pleased with the result and the fact that when we go into the next Yorkshire derby we won't have the monkey on our back.
"I just thought we started the way we should have done but didn't at Sheffield Wednesday and in the end it was fairly comfortable.
"I wanted us to start at a high tempo but we didn't do it and the two goals killed us. It was a long way for us to claw back."