Mowbray was a legendary figure for Middlesbrough at the height of his playing career 20 years ago.
After leading West Brom to promotion last season, Mowbray hopes his side can hold on to their Premier League status.
Three points at the Riverside Stadium should boost confidence but at times Lady Luck was with the visitors.
Middlesbrough struck the crossbar with goalkeeper Scott Carson well beaten and had two goal-line attempts cleared off the line by James Morrison, ironically a product of Middlesbrough's highly-rated Academy.
In the absence of the suspended Emanuel Pogatetz, England international Stewart Downing captained the home team.
West Brom suffered a first minute blow when Kim Do-Heon went down injured. It looked as though the midfield player fell awkwardly, but it was obvious he could not continue and he was stretchered off.
West Brom skipper Jonathan Greening, a former Middlesbrough player, was the first to go into the referee's book for a foul in the 11th minute.
Middlesbrough striker Afonso Alves thought he had ended his lean scoring spell when he played a one-two with Mido, but his fierce shot struck the crossbar.
West Brom were prepared to maintain their reputation of attacking football, but Boro centre-half Robert Huth came close to scoring from a Gary O'Neil corner.
A brilliant Ross Turnbull save denied Jonas Olsson following a Greening corner, before Morrison came to the visitors' rescue when he cleared an Alves header off the line.
West Brom sent on substitute Ishmael Miller, for first-half substitute Sherjill MacDonald and he was involved in West Brom taking the lead through Olsson.
When Turnbull flapped at a Greening corner, Miller passed to Olsson who scored from close range.
Morrison was then the goal-line saviour again when he cleared from David Wheater.
Middlesbrough piled on pressure in a desperate bid to pull the game round, as West Brom battled in defence and were fortunate, while at times they were indebted to brilliant goalkeeping by Carson.
Late breakaways by Miller gave him glorious chances to put the issue beyond doubt, but he failed on each occasion.