In her rookie season, Scanzano appeared in 37 games with 13 goals and 29 assists. Scanzano was the third Quebecer in the history of the Lakers women's hockey program. She was second on the team in assists and third in points. She had nine multiple-point games and ended the season with a seven-game scoring streak. Nationally, she was fifth in points per game by a rookie (1.08), and fourteenth in assists per game (0.73). For her efforts, she was named to the CHA All-Rookie Team and was a six-time CHA Rookie of the Week.
As a sophomore, Scanzano led the team with a .191 shooting percentage while ranking second on team in goals, assists, points, and power-play goals (11). For her efforts, she was named to the All-CHA Second Team. Scanzano’s numbers were the fifth-best single-season offensive numbers in program history. She averaged 2.25 points per game during 16 conference games and was second in conference scoring behind teammate Meghan Agosta. Overall, she ranked sixth in the nation in points scored, and eighth in NCAA Division I in goals and assists
As a junior, Scanzano was named to the 2009-10 Preseason All-CHA team and was also tabbed as the 2009-10 Preseason CHA Player of the Year. During the 2009-10 season, Jesse Scanzano led the NCAA in most shorthanded goals with 4. In addition, she led the NCAA in points per game with an average of 1.97.
Scanzano joined the Montreal Axion as a 15-year-old. Prior to playing for the Axion, she played bantam boys’ hockey in the Lac St. Louis Hockey Association with the West Island Royals. She won the NWHL championship with the Axion in 2005-06. The following season, she was the leading scorer for the Axion as she had 46 points (24 goals, 22 assists) in 35 games.
On February 11, 2007, Scanzano was involved in a controversial game for the franchise. In a game against the Brampton Thunder, Scanzano scored two goals but the game ended in controversy due to the result of the shootout. A player for the Axion left the penalty box prior to the shootout commencing and took the first shot for the Axion. This was a violation of NWHL rules.
Scanzano was the fifth overall selection in the 2011 CWHL Draft. On November 2, 2011, Scanzano was on loan from the Toronto Furies, as she appeared in one game for the Brampton Thunder. The game was an exhibition contest versus her alma mater, the Mercyhurst Lakers. In the second period of said contest, Scanzano scored the game-winning goal as the Thunder defeated the Lakers by a 3-1 tally.
In 2005, Scanzano participated for Team Quebec at the Canadian Under-18 Hockey Challenge. Some of her teammates included future Olympic gold medalist Catherine Ward, future McGill Martlet Ann-Sophie Bettez, and future NCAA players Emmanuelle Blais and Karel Emard.
In 2007, she participated in the European Air Canada Cup for Canada's Under-22 Team. In the first game of the tournament against Japan, Scanzano had three assists.
She represented Team Canada's Under-22 team this week at the 2008 European Air Canada Cup in Ravensburg, Germany.
Scanzano was one of six Mercyhurst players (along with Vicki Bendus, Bailey Bram, Jess Jones, Hillary Pattenden, and Laura Hosier) invited to try out for the Under-22 Team in August 2009. Scanzano was named to the final roster of the 2009-10 National Women's Under-22 Team.
Scanzano won the Gold Medal for the Canadian National Women’s Under-22 Team at the 2010 MLP Cup. In the Gold Medal game, Scanzano had a goal and an assist.
In March 2011, she was invited to the Canadian national women's ice hockey team selection camp to determine the final roster for the 2011 IIHF Women's World Championships.
She travelled to Bratislava, Slovakia to participate in the 2011 IIHF High Performance Women's Camp from July 4–12.