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The Blades had two appeals for penalties turned down in the first half, but there were few clear-cut chances for either side in the opening period.
There was a further blow from United when midfielder Barry Robson was forced off after just 32 minutes with a suspected broken rib.
The home side made a strong start to the second half, and some early pressure resulted in a goal inside the opening two minutes, with substitute Callum McFadzean blasting the ball in for his first goal for the club.
The 19-year-old almost added his second as he raced into the box in the 63rd minute, but Yeovil keeper Marek Stech was able to block his effort.
The teams meet again at Huish Park on Monday for a place in the playoff final at Wembley later this month.