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Kevin Sinfield, successful with all three first-half conversions, also kicked over a 25th-minute penalty to ensure that Leeds were the side in control at Headingley.
A low-scoring start to the second half saw Farrell cross over for the first try, pulling the Cherry and Whites within 12 points of their opponents with 20 minutes left to play.
Kallum Watkins was able to finish off a good team move for try number 19 of the campaign, shortly before Zak Hardaker slotted over his first ever drop goal, but a late push from Warriors allowed John Bateman and Dominic Manfredi to put plenty of pressure on their opponents.
It was not enough, though, with Leeds holding out for the win and retaining top spot in the process.