Nikola Zigic dealt the fatal blow midway through the second half of Sunday's clash when he nodded home from a Sebastian Larsson free-kick to seal the win and move Blues up to 16th.
Substitute Demba Ba rattled the woodwork on his debut but, otherwise, the Hammers rarely threatened the visitors' goal and looked poor throughout.
Grant's position will now undoubtedly come under scrutiny once more as a result.
The Israeli went into the match knowing a victory would see West Ham record their first back-to-back league wins in what has been a troubled season so far.
Their attempts were hit by a calf injury to James Tomkins in the warm-up. That meant an early recall for Matthew Upson, who had missed the midweek win over Blackpool with tendonitis.
The former Birmingham centre-half was paired with Winston Reid , who came in for the injured Danny Gabbidon
Scott Parker assumed his place in midfield the day after he earned a recall to the England squad.
Cameron Jerome and Barry Ferguson both overcame ankle injuries to make a Birmingham team that was unchanged from Wednesday's 2-2 draw against Manchester City.
The match was a chance for the Londoners to avenge their Carling Cup semi-final exit to their midlands rivals last month.
Ben Foster, whose howler gifted West Ham a first-leg lead in that tie, started nervously, punching an early Gary O'Neil cross clear when it was easier to catch.
The England goalkeeper came out to snatch the ball from Frederic Piquionne's feet after he was put through by the in-form Victor Obinna.
After a quiet opening 15 minutes, West Ham started to pressure the visitors' goal.
On-loan Tottenham striker Robbie Keane played Piquionne in with a clever backheel but the former Portsmouth striker could only fire a tame curler at Foster.
Obinna, who had scored five in his previous two matches before today, then struck a 25-yard effort just wide and Parker threatened with a dangerous low cross that was hooked clear.
Robert Green was called into action for the first time when he collected a low shot from Lee Bowyer on the half-hour.
Jerome beat Green to a header from a corner soon after but the former Cardiff marksman could only glance wide.
Roger Johnson beat Piquionne to a cross but flashed a free header over the bar from 10 yards.
Johnson cut out a dangerous cross from Obinna with a superb diving header as Piquionne lurked at the back post.
A late sliding challenge on David Bentley from Mark Noble earned the Hammers midfielder a yellow card.
West Ham felt they should have had a penalty late on in the first half when Lars Jacobsen's strike hit Liam Ridgewell on the arm but referee Chris Foy turned down their appeal.
Obinna had an appeal for another spot-kick turned down moments later when his shot hit Johnson on the arm in the box and Keane volleyed over under pressure in stoppage time.
Manuel da Costa came on for Upson at half-time to make his first appearance in three months.
Birmingham started the second period brightly and Bentley found the towering Zigic at the back post but he headed wide, much to Alex McLeish's frustration.
The Birmingham manager brought Larsson on for Jerome in the 57th minute and Grant replaced Piquionne with Carlton Cole soon after.
The West Ham crowd were getting frustrated with their team's scrappy play and their hopes were further dashed when Zigic gave Birmingham a 65th-minute lead.
The 30-year-old took advantage of some slack marking from Wayne Bridge to meet Larsson's free-kick at the back post and nod home from six yards for his second in two matches.
Foster was booked for time-wasting with 15 minutes remaining.
Grant looked to Demba Ba for inspiration, the Senegalese coming on to make his Hammers debut in place of Keane.
The former Hoffenheim striker almost made an immediate impact when he slammed a volley onto the woodwork after the ball ricocheted around the Birmingham box.
Da Costa almost caught Foster out with a fierce 35-yard shot but the Birmingham keeper scrambled across his line to save.
The defender was at the forefront of West Ham's late push for an equaliser as he headed just wide of Foster's goal from eight yards.
Parker slipped into the box in stoppage time but was met by a sea of Birmingham defenders.
Obinna and Da Costa were booked for late challenges in injury time and West Ham's threat petered out, the game ending with a chorus of boos from the home crowd.
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