The eighth minute incident also produced the game's major talking point.
Darren Way was clearly fouled by keeper Lee Harrison and as the ball ran clear Arron Davies knocked it into the net only to find that referee Mick Fletcher had blown for the penalty.
The official might also have been expected to send Harrison off but he waved a yellow card instead and the Orient keeper was to emerge as man of the match with a series of excellent saves.
Jevons, a summer signing from Grimsby, knocked in his 25th goal from the spot. He has taken 11 penalties and only missed the first which was at Notts County. But even on that occasion he scored from the rebound.
Yeovil had a strong wind in their favour in the first half but needed a second goal to give them a cushion and they always looked like getting it.
Bartosz Tarachulski went close in the 13th minute when Harrison made a good save from a close-range volley and the keeper also saved well from the lively Davies and Paul Terry whose shot in first-half stoppage time struck the keeper's legs.
Yeovil thought they were hard done by in the 19th minute when Andy Lindegaard appeared to be fouled in full flight on the edge of the box. But when Mr Fletcher blew it was to show the Yeovil man a yellow card for diving.
Although the O's had the conditions in their favour in the second half they seldom put Yeovil under real pressure. Their best opportunity came on 72 minutes when a mix-up at the back left Lee Steele clear but goalkeeper Chris Weale earned his bonus by leaving his line smartly to dive at the striker's feet.
Yeovil brought on Kevin Gall for the final seven minutes and he used his pace to set up chances which were missed with wayward finishing.
By that time Orient were down to ten men, young substitute Efe Echanomi being straight red carded in the 79th minute for elbowing Lindegaard - just 14 minutes after coming on.