Blackpool are one point behind their opponents after a disappointing display that saw them fail to compete until Ben Burgess and Stephen McPhee pulled them back into the game.
It took the hosts only 11 minutes to take the lead through an extremely lucky strike from Hungarian midfielder Buzsaky.
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It was Buzsaky's ninth league goal of the season, making the 25-year-old Rangers' highest scorer in their topsy-turvy campaign.
The hosts piled on the pressure and the second Rangers goal arrived five minutes before the break as Vine, stationed wide on the left, picked up a loose ball before driving into the box and stabbing the ball inside the far post.
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Blackpool substitute Burgess pulled one back on the hour, finishing well after Ian Evatt had put him through on Lee Camp.
And just over ten minutes later it was game on as McPhee headed home from three yards after Kaspars Gorkss had headed a corner back across goal.
But Rangers survived to claim the three points that their first-half showing probably deserved.