Boro overcame the loss of central defender Ugo Ehiogu to share the honours.
The former Aston Villa player was shown the red card in the 74th minute for a foul on Liverpool skipper Steven Gerrard.
Ehiogu's departure was a blow to Middlesbrough but Bolton referee Mark Halsey had no alternative but to dismiss him.
The defender was the last player in front of goalkeeper Mark Schwarzer as he brought Gerrard down from behind as the tenacious Reds skipper was in full flight.
A one-match ban will rule Ehiogu out of the home game against Charlton Athletic in a fortnight's time.
Gerrard gave an inspiring skipper's performance that fully deserved his man of the match rating. He had no fewer than seven goal attempts in an all-action display.
It prompted the question "Where were Liverpool's strikers?"
The Reds will have to show more menace if they are to mount a serious challenge to title favourites Chelsea.
Boro gave summer signing Yakubu his debut following his £7million move from Portsmouth.
The Riverside Stadium has not been a happy hunting ground for Liverpool. The Merseyside club have lost on their last three visits and, on an earlier opening day clash, shared a 3-3 draw.
That was the day when Italian ace Fabrizio Ravanelli made a storming entry into English football with a Middlesbrough hat-trick.
Liverpool fans gave an enthusiastic welcome to a team that will go down in history for their sensational European Cup Final comeback in Istanbul. A banner unfurled at the Liverpool end had the words "Rafa joins immortals."
Boro kicked off before a 30,000 plus crowd. There were a few empty spaces in the stand, no doubt due to the fact that the game was being shown live on Sky television.
Not surprisingly, Liverpool winger Boudewijn Zenden was booed by Middlesbrough fans on his return to his former club. A section of the crowd made an uncomplimentary chant over his "greed" following his summer move to Anfield.
However, a move to Liverpool was understandable for a player who won the man of the match trophy in Boro's historic Carling Cup Final win over Bolton Wanderers at the Millennium Stadium.
The prospect of playing in the Champions League is more exciting that the UEFA Cup.
Zenden fired in the opening salvo from 25 yards after three minutes but his effort was easily saved by Australian international goalkeeper Schwarzer.
Gerrard was in the thick of the action from the word go. He prompted his forwards from midfield and then burst through on other occasions to have a pop at goal.
Gerrard, however, was spoken to by the referee after a strong tackle.
After 21 minutes Gerrard had a great scoring chance when a header by Fernando Morientes provided him with an opening. The England international, however, blazed wide. Gerrard would have been disappointed with his effort.
Xabi Alonso picked up the first yellow card with a foul from behind on Jimmy Floyd Hasselbaink. Alonso could have no complaints over his booking.
Ray Parlour then brought down Gerrard from behind. The former Arsenal midfield player protested his innocence with outstretched arms but the referee did not hesitate over his decision.
Yakubu was well held by Liverpool's defence and was a limited threat in the Boro attack with Jose Reina virtually unemployed in the Liverpool goal.
Gerrard continued to dominate the second half and was unfortunate not to pick up a win bonus for his all-round commitment.
Middlesbrough pulled off Yakubu following the departure of Ehiogu and reserve team defender Matthew Bates was introduced to help deny Liverpool a late winner.
MAN OF THE MATCH: Steven Gerrard (Liverpool) – The England midfielder was head and shoulders above any other player. His all-round commitment was outstanding.