Eric Brewer played his junior hockey in British Columbia and by the time he was in midget hockey in Kamloops, realized he may be on his way to fulfilling his dream of playing in the NHL one day. In 1995-96, he joined the WHL's Prince George Cougars and scored 14 points as a major junior rookie defenseman. The following season, he improved to 29 points and played in the mid-season CHL Top Prospects Game. In 1997-98, Brewer was a WHL West Second Team All-Star despite playing just 34 WHL games, recording 33 points. He was selected to play in the mid-season WHL All-Star Game but missed the contest with an injury. He was also an assistant captain for Canada's silver medal World Junior team in 1998.
Brewer was drafted fifth overall in the 1997 NHL Entry Draft by the New York Islanders. One year later, he made his NHL debut on October 10, 1998 against the Pittsburgh Penguins. On November 5, he scored his first goal against the Carolina Hurricanes' Trevor Kidd. Brewer played 63 games that rookie season.
In 99-2000, Brewer played 26 games at the NHL level before he was traded with Josh Green and a second-round draft pick to the Edmonton Oilers for Roman Hamrlík. In his first season, he co-led the Oilers with a +15 plus/minus rating and had 21 points.
Over the course of the next three seasons with Edmonton, Brewer showed the poise and the leadership of a seasoned veteran, bettering his offensive totals each season. In 2003-04, Brewer had his fourth consecutive 20 plus point season with the Oilers before he was dealt to the St. Louis Blues in the summer of 2005 as part of the Chris Pronger trade.
In St. Louis, Brewer provided the Blues with solid, if unspectacular play from the back end. His steady play and calm demeanor made him a natural leader for the young Blues team and on February 8, 2008 he was named the nineteenth captain in franchise history.
On February 18, 2011, Brewer's time with the Blues would come to an end. He was traded to the Tampa Bay Lightning in exchange for a third round draft pick and prospect Brock Beukeboom.
Aside from his World Junior experience in 1998, Brewer captured gold at the 2002 Winter Olympics and represented his country numerous times at the World Championships.