Blues defender Roger Johnson put Alex McLeish's side in front early in the second period.
But Collins made no mistake from close range to salvage a share of the spoils for Villa.
Villa dominated the opening phase and final part of the game and hit the woodwork on three occasions.
But Blues also squandered several clear-cut opportunities.
Blues had defeated Villa in the Carling Cup quarter-final last month but Collins' point-saver means they have not beaten their rivals in a league game for nearly six years.
Villa made a positive start, with Stewart Downing playing just behind John Carew in a 4-1-4-1 formation, and could have taken the lead inside the first minute.
Downing put Blues keeper Ben Foster under pressure and his clearance went straight to Gabriel Agbonlahor.
He cut into the box unopposed but from 12 yards out fired over the bar.
Downing was only just wide with a powerful 20-yard drive as the home side looked nervy.
Blues retaliated and Villa defender Richard Dunne was yellow-carded after chopping down David Bentley in full flight.
Former Villa midfielder Craig Gardner was only just off target with a 20-yard effort.
But Villa looked the more threatening and Carew hit the top of the bar after he flicked on a header from Agbonlahor following a cross by Kyle Walker.
Blues threatened seriously for the first time when Gardner robbed Walker and sent a low ball across the six-yard box but Matt Derbyshire failed to make any contact.
The Blues goal was living a charmed life and Ciaran Clark's cross from the left flank rattled against the crossbar with Foster stranded.
Barry Ferguson teed up Fahey 20 yards out after good play by Alexander Hleb but his shot did not extend Brad Friedel.
The Blues players appealed in vain for a penalty after Marc Albrighton wrestled with Gardner.
But referee Mark Clattenburg waved play on despite strong protests from the Blues players. It was now one-way traffic towards the Villa goal.
Collins cleared off the line from Hleb six minutes before half-time after Stephen Carr had turned the ball across goal.
Villa were the first to threaten at the start of the second half and Carew had a shot deflected wide by Liam Ridgewell from Agbonlahor's low cross.
But in the 49th minute Johnson put Blues ahead after Collins had brought down Hleb 30 yards out.
Gardner failed to make full contact on his low drive but David Murphy flicked the ball on and Johnson applied the finishing touch.
But Johnson was then relieved when he deflected a cross-shot from Clark inches wide of the post as Villa hit back.
Blues almost caught out the visitors on the counter-attack after a mistake by Dunne.
Ferguson played in Derbyshire whose low drive was beaten away by Friedel.
Then a misdirected header from Dunne dropped invitingly for Gardner but he opted to volley first time and was off target.
Carr was booked for bringing down Clark and Foster clung onto a low attempt from Downing.
After 73 minutes Collins brought Villa back on level terms.
Albrighton's centre found its way to the Welsh international and his shot took a deflection off Ridgewell before beating Foster.
Foster made a fine save to deny Downing after Nathan Delfouneso rolled the ball into his path.
Ridgewell came to City's rescue when he cleared Dunne's header off the line from an Albrighton centre.
Villa were now in control and Foster tipped a dipping drive from Delfouneso onto the bar.
In injury time Blues substitute Nikola Zigic outjumped Friedel but headed inches wide.