The 2000–01 NHL season was Daniel's first season with the Canucks. His debut was the team's first game of the campaign on 5 October 2000, a 6–3 loss to the Philadelphia Flyers. Daniel and Henrik became the fourth pair of twins to have played in the NHL. Three days later, Daniel scored his first career NHL goal against goaltender Dan Cloutier of the Tampa Bay Lightning. Assisted by Henrik, the goal tied the game at 4–4 with 1:13 minutes left to go in a 5–4 regulation win. On 30 November 2000, he suffered a shoulder injury, sidelining him for four games. During his recovery, he was reprimanded by Canucks head coach Marc Crawford, who told him that playing through pain is part of being in the NHL. Later in the season, he missed an additional three games due to a back injury, shortening his rookie season to 75 games. He became the first rookie in 2000–01 to reach 20 goals when he scored on 21 March 2001, in a 1–1 tie against the Columbus Blue Jackets. Finishing the campaign with that goal total, he tied for second among League rookies in scoring with Shane Willis, behind Brad Richards. He also had 14 assists for 34 points in total. Making his Stanley Cup playoff debut against the Colorado Avalanche, Daniel recorded an assist in the opening game of the first-round series, a 5–4 loss for the Canucks. He added his first NHL playoff goal later in the series as the Canucks were eliminated in four-straight games. He and Henrik played primarily on the Canucks' third line. Daniel received one third-place vote from the Professional Hockey Writers' Association for the Calder Memorial Trophy as NHL rookie of the year, finishing eighth in award balloting overall.