Elliott now faces a three-match ban after his red card for a forearm challenge on David Dunn.
Adams had to see out the rest of the game from the main stand after he allegedly verbally abused referee Mike Riley as the sides left the pitch at half time.
Then, on the hour mark, City were reduced to nine men when Walker got his marching orders for handling the ball outside the penalty area.
As early as the first minute Maik Taylor cut his mouth and needed attention after a challenge by Les Ferdinand.
All the early pressure came from the home side but their attacks lacked a cutting edge.
Birmingham had to wait until the 15th minute for their first meaningful effort on goal when Clinton Morrison forced a diving save from Walker.
Robbie Savage, returning to his former club for the first time since joining Birmingham, was then fortunate to escape punishment after a scything tackle on Andrew Impey.
It was hardly a spectacular game and the referee did little to keep play flowing by awarding a string of free kicks for petty offences.
But the contest came alive for the wrong reasons on 37 minutes when Elliott was shown a straight red card after catching Dunn in the face with a forearm during an aerial challenge.
And there was further misfortune for the Foxes three minutes later when the visitors carved open a depleted defence to take the lead.
Dunn played the ball through to Jamie Clapham whose low cross was turned in by Morrison from six yards.
A clearly angry Adams had to be shepherded away at the half-time whistle as he appeared to seek to approach the referee who left the pitch to a crescendo of boos.
And there was further controversy when it emerged that during the interval Adams had been sent from the technical area for his apparent outburst at the referee.
Elliott's dismissal led to a half-time reshuffle with John Curtis coming on for Ferdinand as Leicester opted to play three at the back with Impey moving to midfield and James Scowcroft switching to attack.
But disaster struck Leicester on the hour mark when they were reduced to nine men after Walker was sent off for handling the ball outside his area.
The referee was left with no alternative when the keeper's attempted clearance rebounded off Mikael Forssell and Walker then made the fatal error of instinctively grabbing the ball.
The home side withdrew Paul Dickov and sent on substitute keeper Danny Coyne whose first significant contribution came on 65 minutes when he was picking the ball out of the net after Forssell had headed home a Savage cross.
Birmingham should have buried the home side on 73 minutes, but substitute Stan Lazaridis fired wide from close in with only the keeper to beat.