The two sides have similar records in the Premiership and both have poor records in the FA Cup with Charlton attempting to reach the semi-final for the first time in 59 years.
But the two sides managed just one shot on target apiece and it will be the 12th April when this tie will be decided with a replay at The Riverside.
Middlesbrough were playing their 19th cup tie of the season and put out their strongest side with Steve McClaren making seven changes from the team that lost at Blackburn while Charlton boss Alan Curbishley reverted to a more attacking 4-4-2 system but it failed to bring the desired result with his strikers often being isolated for long periods.
Yakubu could have scored as early as the third minute when he was given a free header which he put over the bar but it was Charlton who slowly took control in the opening 45 minutes and produced what little chances there were.
The best fell to Hermann Hreidarsson whose volley produced the finest save of the match from Mark Schwarzer. Darren Bent also went close for the home side.
The match was always going to be tight and the first goal was likely to be decisive but neither side had the guile to open up their opponents defence and the chances became less and less as the game progressed.
Mark Viduka, who loves scoring against Charlton, replaced Yakubu and brought more balance to the Middlesbrough side but it was not until the last 20 minutes before Charlton keeper Thomas Myhre was forced into making a save, turning substitute James Morrison's shot behind for a corner.
Having beaten Middlesbrough twice this season Charlton would have hoped that they could have made it a hat-trick of victories but having won 3-0 at the Riverside Stadium at the beginning of the season they will still be confident that they can reach the semi-final as Boro have a hectic UEFA Cup programme ahead of them.
Off the field Charlton have announced a £5.1million loss in the six months to December 2005 and chairman Richard Murray believes the Premier League has reached a critical point in its evolution.
He is not happy at the over-exposure of the League on television, the disparity of kick-off times and his views certainly seemed to be reinforced by the fare served up on this Thursday night.