Wrexham extended their unbeaten run to seven games when the third division's top scorer Andy Morrell fired home a penalty midway through the first half.
It was Morrell's 34th goal of the season and left Wrexham still in with a chance of grabbing the runners-up position.
But it was West Midlands referee Mark Cooper who stole the headlines when he harshly dismissed Leyton Orient defender Justin Miller who had tripped Lee Trundle in the box to concede the spot kick.
After the game O's manager Paul Brush fumed: "Justin Miller said he never touched the boy and even when the referee gave the penalty it never occurred to me that he would be sent off.
"It was a decision that wrecked the game and nine out of ten times would never have been given." However, Brush was delighted with his side's brave showing against already promoted Wrexham and added: "I thought it was a gritty, determined performance as we had to play for 70 minutes with ten men against a very good Wrexham side.
"Overall I was really pleased. I don't feel down at all with the level of passion we showed. It was just a shame we couldn't nick a draw." Orient started well and Gary Alexander saw his early effort cleared off the line by Brian Carey.
Morrell justified his top scorer's tag with a fierce drive that Glenn Morris did well to save, but minutes later Morrell was celebrating when he fired home from the spot.
After the break Carlos Edwards went close to breaking down ten-man Orient but the home side almost levelled when Wayne Purser and Chris Tate fired in fierce shots.
Wrexham boss Denis Smith said after the game: "After the sending off we became casual and fair play to Leyton Orient they had a right go at us."