Justin Meram tied it for the Crew (3-4-2) in the 67th minute, 4 minutes after Dallas' Zach Loyd was sent off for a second yellow card for his tackle on Meram.
''I shot as hard as I could,'' Miranda said. ''The important thing for me is the win. We needed the three points. That's better for the confidence of the team.''
The veteran of nearly 10 years in his native Chile scored for the first time in 43 games since joining the Crew last season. He got the goal on a sitting, snap header from just outside the penalty area off a cross from Nemanja Vukovic.
''We practice some plays but maybe not like this,'' Miranda said. ''The idea was from the middle, outside the box. I was alone.''
FC Dallas coach Schellas Hyndman thought the second caution to Loyd when he elbowed Meram was fair but questioned other calls.
''There were two or three hits that could have stopped the whole play,'' Hyndman said. ''Those are the calls they aren't made that eventually come into something else.''
Meram made Dallas pay when he struck from 35 yards after teammate Eric Gehrig stole the ball from Matt Hedges.
''I like the goal I scored but you have to win,'' Meram said about scoring for the first time 19 career MLS games. ''If we tied and I scored I wouldn't be this happy.''
Fabian Castillo put Dallas (3-6-3) ahead in the 22nd minute with his first goal of the season.
The Crew snapped a six-game winless streak, while Dallas dropped to 0-3-3 in its last six.
- Columbus Crew
- Justin Meram
- FC Dallas
- Zach Loyd