Neither side ever really looked like breaking the deadlock in a dull stalemate as Middlesbrough made it five points from a possible nine this season, while the Baggies are just one point behind.
Both sides went into the match looking to bounce back from EFL Cup exits to lower-league opposition in midweek, but clear chances were few and far between in a tight and uneventful opening 45 minutes.
West Brom, now winless in six Premier League outings at The Hawthorns, looked most like scoring in the first half, but were forced to settle for half-chances mostly, the first of which saw Jonny Evans fail to properly connect with a volley from a corner.
The best chance of the half came in the 12th minute when James McClean got on the end of Darren Fletcher's clipped ball forward following a good team move, but Brad Guzan was quickly off his line to thwart the winger from a tight angle.
Salomon Rondon was the next to have a sight of goal when he got on the end of a cross from the left flank, but the ball arrived behind him and he could not steer his header on target.
Boro went into the match having conceded fewer league goals than any other side in the top four tiers of English football since the start of last season, and they rarely looked like being breached in the first half despite their lack of attacking intent at the other end of the field.
Brendan Galloway, making his Premier League debut for the club, drew a rare stop from Guzan towards the end of the half, but it was a routine save from the former Aston Villa keeper as he got down to keep out the low drive.
The Baggies stepped up the pressure in the closing stages of the half, but Rondon twice fell just short of connecting with crosses into the box, the latter coming after Guzan had completely missed an attempted punch from a corner.
Middlesbrough finally registered their first shot of the match shortly after the interval when Gaston Ramirez was played into a bit of space down the right channel, but he had no support and could only slice his effort wide of the near post.
Boro knew that a goal could be enough to hand them back-to-back Premier League away wins for the first time in over a decade, when they also beat Sunderland and West Brom in succession, and they finally created their first real chance of the game with just over 15 minutes remaining when Antonio Barragan stormed forward before finding Ramirez, who could only place his finish straight at Ben Foster.
It was the visitors' first shot on target all afternoon, but they were back on the front foot 10 minutes later as Stewart Downing came forward before driving an effort past the far post.
In the end, though, neither side could break the deadlock as the two teams were forced to settle for a point apiece - a result that drew boos from the home fans upon the final whistle.
The Baggies are now unbeaten in their last seven league and cup meetings with Middlesbrough and have kept five clean sheets in a row against the North-East outfit.