Born in Córdoba, Córdoba Province, Bergessio started his career in the lower leagues with Club Atlético Platense. In 2005 he was signed by Instituto Atlético Central Córdoba of the Primera División, but at the end of the 2005–06 season Instituto were relegated, and the player was sold to Racing Club de Avellaneda.
During the Apertura 2006 Bergessio contributed with six goals, and in the following year's Clausura, continued to score on a regular basis. His fast pace earned him a big following at the Estadio Juan Domingo Perón, and he became a fan favourite after scoring the game winner against giants Boca Juniors, adding another against Club Atlético River Plate.
On 26 June 2007, Bergessio signed a five-year deal with Primeira Liga club S.L. Benfica for a reported €2.5 million fee, as an unknown party remained eligible to 50% of the future transfer fee the Portuguese received. He only appeared in three league matches during his spell, one more than his opportunities in the UEFA Champions League, and, in January of the following year he returned to his country.
In January 2008, Bergessio joined San Lorenzo de Almagro. On 8 May, he was involved in the Copa Libertadores tie against River where, after his team had two players sent off and were 0–2 down, he scored twice to give it an improbable aggregate win.
On 25 August 2009, Bergessio returned to Europe by agreeing to a four-year contract with France's AS Saint-Étienne, for an undisclosed fee.
He scored his first goal for his new club during his second appearance, a 1–1 home draw against AJ Auxerre, but netted just five times more in his first one-and-a-half seasons with the Ligue 1 club.
In the last hours of the 2011 winter transfer window, Bergessio joined Italian side Calcio Catania, arriving on loan for the remainder of the season – the Sicilians had the option to sign him player permanently at the conclusion of this loan agreement. He made his Serie A debut on 20 February, playing the full 90 minutes and being booked in a 0–1 away loss against S.S.C. Napoli.
After an initial delay in the transfer, Bergessio signed with Catania permanently on 29 August 2011, for €945,000 and a four-year contract. In the 2012–13 campaign he became a key part of Rolando Maran's team, forming an efficient offensive partnership with countrymen Pablo Barrientos, Lucas Castro and Alejandro Gómez; on 5 May 2013 he scored his first hat-trick in Italy's top flight, in his team's 3–0 home win over A.C. Siena.
Bergessio helped Catania eventually finish in eighth position, with a record in total points for the fifth consecutive season. On a personal level he was also the club's highest goalscorer during a single campaign, since Gionatha Spinesi netted 17 times in 2006–07.
On 30 October 2013, Bergessio suffered a broken fibula as a result of a late tackle by Giorgio Chiellini in Catania's 0–4 loss at Juventus FC.
On 1 August 2014, Bergessio was sold to Serie A club U.C. Sampdoria for a fee of €2.65 million, putting pen to paper to a three-year deal. On 3 June of the following year, after 24 appearances all competitions comprised and two goals, he was released by mutual consent.
On 24 June 2015, Bergessio moved teams and countries again, joining Club Atlas from Mexico. The following 8 September, he signed a one-year deal with former club San Lorenzo.
Bergessio made his international debut on 15 October 2008, playing the second half of a 0–1 loss in Chile in the 2010 FIFA World Cup qualifiers. He scored his first two international goals on 20 May of the following year, in a 3–1 win over Panama.