He played junior hockey for the Ottawa Aberdeens in 1893 before joining the senior level, fledgling Ottawa Hockey Club for the 1894-95 season. The club had been formed in 1893, but hockey was in such a state of infancy at the time that they were the first club in all of Ontario, and as such, had no opponents to play against!
Westwick actually started as the club's goaltender for his first pair of games, a win and a loss. Westwick would score his first goal for the club that season after being moved up to the rover position after his quick skating ability was recognized.
During the summer he played lacrosse for the Ottawa Capitals, who were accused of paying their players. Those accusations got Westwick suspended from the hockey club. He denied the charges and was reinstated. Eventually, he would play in 8 games of the 1895-96 season, scoring 8 goals. He would play another 8 games in 1896-97, scoring 6 goals that season. After scoring a single goal in five games of the 1897-98 season, accusations of player payments once again arose, the Westwick would again be suspended by the Canadian Amateur Athletic Union.
Westwick returned to the Ottawa Hockey Club for the 1900-01 season with his scoring touch still intact, as he registered 6 goals in 7 games that season for eighth overall in the Canadian Amateur Hockey League. The 1901-02 season saw him hit double digits for the first time, scoring 11 goals in 8 games to lead the club in scoring and finish third overall in the CAHL.
For the 1902-03 season, Westwick contributed 6 goals in 6 games, as Ottawa finished tied atop the standings with the Montreal Victorias at 6-2, which necessitated a playoff. The first game ended tied at 1-1, but Ottawa stormed to an 8-0 victory in Game 2 to lay claim to the first Stanley Cup in team history. Two days after earning the rights to the cup for surpassing the Victorias as CAHL champions, the Ottawa Hockey Club would have to defend their new trophy against the Rat Portage Thistles, who they easily defeated 6-2 and 4-2 for a 10-4 win in the two-game, total goals series.
The Ottawa Hockey Club players would each receive a silver nugget for their championship, which quickly led to the team becoming known as the Ottawa Silver Seven. While Westwick was limited to only two games of the 1903-04 regular season, he would score 5 goals. The Silver Seven would controversially leave the CAHL during the season, but the trustees of the cup ruled that it belonged to Ottawa and not the eventual winners of the CAHL.
During the early part of the CAHL season, Ottawa would defend the cup from a challenge made by the Winnipeg Rowing Club. Westwick led Ottawa with 4 goals during their opening 9-1 win. Winnipeg rebounded with a 6-2 win in Game 2, although Westwick had one of the two Ottawa goals. They then retained the Stanley Cup with a 2-0 win in the decisive Game 3.
1904 would also see the end of Westwick's lacrosse career, which began in 1896, and included three world championships with the Ottawa Capitals club, the final one coming in 1901.
Ottawa became members of the Federal Amateur Hockey League for 1904-05, Westwick's finest, as he set a career high with 15 goals in 6 games, placing third in league scoring. Following Ottawa's league championship, they took part in the most famous Stanley Cup challenge ever, as the Dawson City Nuggets traveled 4,000 miles from the Yukon, a journey which took a month and included travel by dog sled, bicycle, several hundred miles on foot, steamship and eventually a train. Game 1 went to the champion Silver Seven 9-2 with Westwick contributing 2 goals before Game 2 turned into a farce, with mighty Ottawa winning 23-2 with Westwick adding 5 goals to teammate Frank McGee's 14.
For the 1905-06 the CAHL and the FAHL came together to form a new league, which was named the Eastern Canada Amateur Hockey Association. During the ECAHA season, The Silver Seven defended the cup with a pair of dominating 16-7 and 12-7 wins over Queen's University in late February, with Westwick scoring four during the first game. Just prior to the end of the regular season, another challenge from Smiths Falls was turned away after a 6-5 and an 8-2 win game them a two game sweep in their best-of-three series.
The ECAHA season ended with the Silver Seven and the Montreal Wanderers tied with 9-1 records, setting up a championship playoff with the cup on the line. A 9-1 win in Game 1 gave Montreal a huge advantage in their two-game, total goals series. Still, Ottawa fought back in Game 2. While the Wanderers scored the first goal of the game, three Ottawa goals cut the deficit to 10-4. After another Ottawa goal to open the second half, Westwick scored twice to narrow the margin to 10-7. Three straight goals by Harry Smith evened the series at 10-10, leading to a five minute standing ovation by the home fans. Smith was then penalized and sent off for the remainder of the game and Lester Patrick scored the game winner for Montreal with a minute and a half left to play before adding another with just seconds remaining to end the three year long Ottawa stranglehold on the Stanley Cup which lasted from March 10, 1903 through March 8, 1906 and included the successful defense of nine challenges.
Westwick scored 14 goals in the 9 games of the 1906-07 season for Ottawa, and then their season concluded, he joined the Kenora Thistles for their final regular season game and then participated in their Stanley Cup defense versus the Wanderers.
For the 1907-08 season, Westwick was back with the Senators, scoring 10 goals in 10 games before one final season of play in 1908-09, scoring 3 more goals in 6 games played.
He would total 92 goals in 93 regular season games as well as 25 more goals in 24 playoff and Stanley Cup challenge games. Westwick was elected to the Hockey Hall of Fame in 1963, giving him the last laugh over the journalist who dubbed him a "miserable, insignificant rat".