Albion were the more progressive side but visiting goalkeeper Brad Guzan saved comfortably from James McClean and defender Brendan Galloway.
The home side might have had a penalty when striker Salomon Rondon clearly had his shirt held by Ben Gibson and Albion's Craig Dawson headed narrowly wide from a corner in the second half.
Middlesbrough, promoted last season under Spaniard Aitor Karanka, took 73 minutes to have a shot on target but held on to maintain their unbeaten record after three games.
That took them into joint sixth place with Tottenham, ahead of the later game between Manchester City and West Ham.
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It was a generally solid performance but one lacking attacking threat, despite the vigorous efforts of Alvaro Negredo, the former Manchester City striker signed on a season's loan from Valencia.
He set up the one shot on goal, by Cristhian Stuani.
"It was an important point," Karanka told Sky Sports.
"West Brom is a difficult place so I am pleased with the players. The discipline was good and the second half in particular it was not easy to play the way we wanted."
Albion manager Tony Pulis has said he wants five more players before Wednesday's transfer deadline.
"I thought we played really well the first 25 minutes, we didn't get a goal and then it petered out," he said.
"We need that bit of quality, we are working hard and hopefully we can do it. This is a great group of players but we are squeezing everything out of them."
(Reporting by Steve Tongue, editing by Ed Osmond)
