Acton was selected 103rd overall by the Montreal Canadiens in the 1978 NHL Amateur Draft. He began his NHL career on Montreal's fourth line but his productive play soon earned him a promotion to the first line, where he centered all-stars Steve Shutt and Guy Lafleur. He became known as one of the best faceoff men in the NHL. His most productive NHL season came in 1981–82 when he registered 88 points in 78 games with Montreal. When his production dipped the following year to just fifty points, his stock in Montreal fell and early in the 1983-84 campaign, Acton was part of a blockbuster trade. The Canadiens packaged Acton up with Mark Napier and a third pick and dealt them to the Minnesota North Stars for Bobby Smith. With Minnesota, Acton reeled off three consecutive 20-goal seasons but after a slow start to the 1987-88 season he was dealt to the Edmonton Oilers. With Edmonton and their high-powered offence, Acton was not expected to help carry the offence and settled into a more defensive role. That spring he won the Stanley Cup though he played just seven games in the post season. Acton was a healthy scratch through the first two rounds and remained in the pressbox through the first three games of the conference final against the Detroit Red Wings. However, with the Oilers' coaching staff looking for more speed on their fourth line, Acton was inserted into the lineup for game four and he paid immediate dividends, scoring the series-clinching goal. His clutch play continued in the Stanley Cup final when he ended game one against the Boston Bruins by tipping a Steve Smith point shot for the game winning goal. Despite his playoff heroics, it still proved difficult to carve out a place on the Oilers' deep roster and late in the 1988-89 season, his second in Edmonton, he was on the move again when he was traded to Philadelphia in exchange for tough guy Dave Brown. Acton spent the next four seasons with the Flyers providing veteran leadership and depth down the middle. For the 1993-94 season Acton signed a deal to join the Washington Capitals but found himself on waivers after just six games in D.C. and was claimed by the New York Islanders. With the Isles, he played out the rest of the season before retiring.
Personal life
Acton's son, Will, is also a hockey player. Like his father, Will played parts of two seasons with the Edmonton Oilers. Will now plays for the Schwenninger Wild Wings of the DEL. In 2018, Acton became a candidate for mayor of Whitchurch-Stouffville, Ontario, in the Ontario municipal elections in which he came in second.
Season Team Lge Type 1994-95 Philadelphia Flyers NHL Assistant 1995-96 Philadelphia Flyers NHL Assistant 1996-97 Philadelphia Flyers NHL Assistant 1997-98 Philadelphia Flyers NHL Associate 1998-99 New York Rangers NHL Assistant 1999-00 New York Rangers NHL Assistant 2001-02 Toronto Maple Leafs NHL Assistant 2002-03 Toronto Maple Leafs NHL Assistant 2003-04 Toronto Maple Leafs NHL Assistant 2005-06 Toronto Maple Leafs NHL Assistant 2006-07 Toronto Maple Leafs NHL Assistant 2007-08 Toronto Maple Leafs NHL Assistant 2008-09 Toronto Maple Leafs NHL Assistant 2009-10 Toronto Maple Leafs NHL Assistant 2010-11 Toronto Maple Leafs NHL Assistant 2013-14 Edmonton Oilers NHL Assistant