Allen, 26, twice capped by England, was left unconscious on the ground for several minutes after a high tackle from Bath's giant centre Matt Banahan, one of three players to be sent off by referee Tim Wigglesworth in five minutes of mayhem.
First to go was Bath flanker Francois Louw in the 60th minute for use of the elbow. Banahan followed after the tackle on Allen, as did Leicester flanker Brett Deacon for retaliation.
Bath also saw No 8 Simon Taylor and fly-half Stephen Donald sin-binned in the 50th and 67th minutes respectively, indiscipline which helped Leicester fight back from 12-6 down at the end of the third quarter to win 17-12.
Leicester director of rugby Richard Cockerill said: "Anthony is sat up in the changing room, he is dazed but he will be okay."
Bath head coach Toby Booth said the game was "one of the most surreal experiences" of his career.
He added: "I am a bit shell-shocked. When you come to Welford Road you have to be extremely competitive and we spoke about that a lot this week.
"Self-control is part of a professional player's make-up. Some of the issues we saw out there were self-control issues, others were consistency issues.
"I am not going to stand here and say it should not have been (red card). I did not see Francois' incident, it was off camera.
"Allen ducked into a tackle from Banners and he has caught him high.
"We are bitterly disappointed because we thought we had an opportunity today."
Cockerill had some sympathy for all three players who were sent off.
He said: "Banahan is a big man, he's not a dirty player. He has gone in and hit him high.
"The laws are a bit mad. If Louw has dropped an elbow on someone is it a red? Probably not. It might be a yellow, but that's the world we live in.
"Banahan hits a bloke and knocks him unconscious, but it looks a lot worse than it is. Brett Deacon retaliates and he is off.
"If you go back to the 1990s when this side was very aggressive we would have three blokes a side. I don't necessarily agree with how it's refereed but that's the way it is."
Before the dismissals Bath were leading 12-6 thanks to tries by Donald and Tom Biggs, which Donald converted.
After it Leicester scored a try through Adam Thompstone and fly-half George Ford added two more penalties to the two he kicked at the start of the second half.
Leicester's win puts them back on track for the play-offs after last week's defeat at Wasps, while Bath will be kicking themselves for their indiscipline having beaten league leaders Harlequins in their previous game.
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