After 97 days with the "Iron" he moved on to Coventry City for a £60,000 fee, after impressing in a reserve team game between the two clubs. The management team of George Curtis and John Sillett offered Houchen £350 a week, £50 an appearance, a £10,000 signing-on fee, as well the chance to play First Division football. He struggled with injuries at the start of the 1986–87 campaign, but recovered to ensure his name went down in the club's history for his exploits in the FA Cup. He bagged five goals in their 1986–87 cup-winning run, the first being the winning goal away at Old Trafford against Alex Ferguson's Manchester United. He then scored two against Sheffield Wednesday in the quarter-finals, and one against Leeds United in the semi-finals, both games being held at Hillsborough. The final and most famous goal of the run came in the 1987 FA Cup Final in front of 98,000 spectators at Wembley Stadium in a 3–2 win over Tottenham Hotspur. However Houchen almost missed the match after catching food poisoning from a trout caught by reserve goalkeeper Jake Findlay. The goal came from a Dave Bennett cross and was an instinctive full-stretch diving header that was impossible for Ray Clemence to save. It levelled the score at 2–2 on 63 minutes, and an own goal from Gary Mabbutt in extra time won the game for Coventry. As well as his FA Cup winning medal, Houchen's header also earned him the BBC Match of the Day's Goal of the Season award for the 1986–87 season. This was due to the acrobatic effort involved and partly due to the incredible run he had made from deep midfield to meet the crossed ball. It is generally considered as one of the most famous goals scored at Wembley, and certainly the best headed goal.