Premier League - City cling on to draw at Liverpool
Mario Balotelli was sent off for two bookable offences within 18 minutes of coming on as a substitute, leaving the visitors to see out the final 10 minutes a man down.
The match was overshadowed by the tragic news of Wales coach Gary Speed's death.
Kenny Dalglish removed Craig Bellamy from the Liverpool squad because the Welsh striker was so upset about the passing of his manager, friend and mentor.
A minute's silence preceded the match and the name of Speed, a former Evertonian, rang around Anfield as the teams kicked off.
Liverpool played a solid 4-5-1 formation with Luis Suarez on his own up front, supported from the flanks by Dirk Kuyt and Stewart Downing, and it was the Reds' strength in midfield that enabled them to dominate possession early on without creating a clear-cut chance.
At the other end, Yaya Toure blazed a left-foot shot on the turn high and wide, while the tricky footwork and intelligence of Aguero and David Silva started to pull Martin Skrtel and Daniel Agger out of position.
Kompany gave City the lead just after the half-hour mark, profiting from some woeful marking at a corner - the Belgian rose to glance the ball into the top-left corner almost unchallenged, though it appeared to go in off his shoulder.
But within seconds, Liverpool were level. Charlie Adam's shot was heading wide but Lescott - perhaps fearing the presence behind him of Kuyt, stuck out a boot and diverted the ball past the helpless Joe Hart.
The home side were still without a shot on target, yet somehow on terms.
Adam finally tested Hart from the edge of the box after great work by Kuyt on the left side. Hart's momentum was taking him the wrong way, but he still managed to make a fine save with his feet.
Liverpool continued to have the better of things after the break, and Kuyt might have done better with his header on 52 minutes, but he headed into the ground when Downing's deflected cross came to him.
Then Downing hit a volley into the ground that nearly looped over Hart and in on the second bounce, but the keeper made a fine save.
Balotelli came on with 65 minutes on, but his cameo was short-lived - he was red carded following bookings for a tug on Glen Johnson and for leading with the arm on Skrtel.
The Italian will be suspended for City's Carling Cup game against Arsenal, and was reportedly involved in a post-match scuffle that left the visiting dressing room door damaged.
Both sides had late chances to win it - Suarez brought another stop from the excellent Hart, while Silva might have converted on the counter-attack for City but took an age to round Pepe Reina, by which time Liverpool had three players back on the line.
In the 93rd minute, substitute Carroll looked to have won it with a powerful header from Glen Johnson's cross, but Hart clawed it behind with a final exceptional act.