However Birmingham were rewarded for a battling display when Scotland striker Garry O'Connor equalised three minutes after the break to take a valuable away point.
Liverpool moved up to fourth on goal difference with their point at the Riverside, but that will be small consolation for under-pressure boss Rafael Benitez after his side missed a golden opportunity to close the gap on Arsenal.
Boro took the lead midway through the first half when George Boateng fired home from close range after a knockdown from Turkey forward Tuncay Sanli.
A superb strike from Fernando Torres, his 17th goal of the season, got Liverpool back on level terms but, despite intense late pressure, they were unable to find a winner and sit on 39 points, equal with Everton, Aston Villa, and Manchester City.
"To draw away is sometimes good but when you want to win it is not so good," Benitez lamented after the match.
Chelsea down Spurs
Chelsea took full advantage of Arsenal and Liverpool's slip-ups when they easily accounted for Tottenham 2-0 thanks to goals from Juliano Belletti and Shaun Wright-Phillips at Stamford Bridge.
The Blues left new striker Nicolas Anelka on the bench for almost an hour but were still too good for Spurs after Belletti scored an absolute screamer on 19 minutes, and Wright-Phillips ended any doubt over the outcome ten minutes from time.
Anelka, who signed earlier in the week from Bolton, almost marked his debut with a goal when his shot on the turn in the closing minutes struck the under-side of the bar.
Meanwhile at Goodison Park, Joleon Lescott made up for the own goal he scored in his club's League Cup semi-final defeat at Chelsea in midweek by scoring the only goal in Everton's win over Man City.
It was a defeat which saw City slip from fourth to seventh on the table on goal difference.
Villa up to sixth
Aston Villa forward John Carew bagged a brace
in a 3-1 win over Reading [GALLO/GETTY]
Aston Villa maintained their push for a place in Europe next season with a comfortable 3-1 win over Reading which lifted Martin O'Neill's side to the lofty heights of sixth place.
A John Carew double either side of a Martin Laursen strike secured the points with James Harper scoring a consolation goal for Reading in stoppage time.
At Upton Park, second-from-bottom Fulham's woes deepened as they once again squandered a lead and succumbed to a 2-1 defeat against West Ham.
Simon Davies gave the Cottagers a ninth-minute lead, but Dean Ashton boosted his chances of a return to the England squad next month by heading in a 28th-minute equaliser before Anton Ferdinand volleyed the winner with 20 minutes left.
Finally at Pride Park, Antoine Sibierski's 82nd-minute strike was enough to earn Wigan a valuable 1-0 win over ten-man Derby which lifts Steve Bruce's side three points clear of the relegation zone.
Derby played most of the second half a man down after defender Claude Davis was sent off for a second bookable offence.
Manchester United have the chance to return to the top of the table on goal difference, if they can beat Newcastle at Old Trafford in Saturday's late kick-off.