Jermaine Johnson and Leroy Lita both had early chances for the home side, but it was Steve Howard who gave Wednesday the lead after just nine minutes, firing the ball in from outside the penalty area.
Lita doubled the hosts' advantage just before the half-hour mark, heading in from a Lewis Buxton corner.
Both sides had chances at the start of the second half, as Grant Leadbitter forced a save from Chris Kirkland, before Jason Steele had to make a stop at the other end moments later as Lita looked for his second.
Leadbitter continued to look threatening for the visitors, testing Kirkland again before forcing a clearance from Anthony Gardner.
There were few chances towards the end of the game, as both sides seemed happy to settle for the result.
The result leaves Wednesday 18th in the Championship table, while Middlesbrough finish 15th.