Woods was selected in the first round of the 1987 NFL Draft. In 1988, he recorded career-highs with 141 total tackles and five sacks. Woods made a memorable impact during the 1990 season, forcing a fumble in overtime against the Houston Oilers, which led to a game-winning recovery by Dave Wyman. The win made Seattle just the third team in NFL history to win back-to-back overtime games. After seven seasons with the Seahawks, Woods played for four more years with Los Angeles and Washington. He finished his career with 697 total tackles, 24.5 sacks, and eight fumble recoveries.