Becchio, making his first start for Leeds, beat home skipper Terry Skiverton for speed and fired a low drive past goalkeeper Asmir Begovic.
But Yeovil hit back in a match marred by a multitude of fouls and seven bookings with an equaliser after 62 minutes.
Paul Warne was fouled by Paul Huntington and referee Dean Whitestone awarded the Glovers their first penalty for two years.
Substitute Lloyd Owusu saw his shot blocked by Casper Ankergren, but the big striker followed up to net the rebound.
In the closing minute Yeovil almost snatched victory, with Gavin Tomlin going close on two occasions, his best effort a lob which almost caught Ankergren off his line. The draw is a decent point for Yeovil, who have made a surprisingly good start to the season with their paper-thin squad.