He began his career with Barranquilla F.C., Atlético Junior’s second division team in 2006. After scoring 16 goals in 28 appearances, he was called up to Atlético Junior senior team.

In his first years with the main squad, Gutiérrez found it difficult to break into the starting eleven. He managed to score his first goal on 2 September 2007 in a match against Malaga. During Copa Mustang in 2008, he earned a spot in the starting lineup and managed to score 11 goals, finishing third place in the scoring charts, just behind Freddy Montero and Carlos Quintero and tying Adrián Ramos and Milton Rodríguez.

Gutiérrez scored in his international debut in 2–1 on his debut Colombia victory against El Salvador in August 2009. In his third call up to the Colombian national team, he made his first competitive appearance in a qualifying game for the 2010 FIFA World Cup against Ecuador, scoring the second goal in a 2–0 victory.

On 13 January 2010, Junior sold Teo to Turkish club Trabzonspor for $3 million. During his first season in Turkey, he found it difficult to adapt to a new country and style of play, which led him not being a regular on the starting eleven.

Gutiérrez moved to his country without permission of Trabzonspor or his manager claiming to have some health problems. After check-ups, doctors did not find any health problems, and on 3 February 2011, Trabzonspor accepted a bid from Racing Club of Argentina.

Teo was sold to Mexican side Cruz Azul by US$3 million and a salary of US$1.5 Million per year. Despite being used as a substitute of Argentine striker Mariano Pavone for most of the season, he managed to score important goals for Cruz Azul in the Liguilla while Pavone was injured, including one in the final against América which they lost. After a six-month spell at Cruz Azul, Teó said we wanted to leave to Argentinian side River Plate, even though he initially expressed his will to stay at the Mexican club. After being separated from the first squad he was finally sold to River Plate in July 2013.

He made his debut in a 2–1 loss against Club Atlético Colón. where he scored his very first goal. He would later be part of the team that crowned itself champion in the following tournament, scoring 6 goals. Under the management of Marcelo Gallardo, Teo has scored 10 goals in 10 appearances (missed two fixtures due to being called up by the Colombia National Team) in the 2014 Torneo de Transición.

During the 2014 FIFA World Cup qualifiers, Gutiérrez scored six goals in 11 matches. In June 2014, he was named in Colombia’s squad for the 2014 FIFA World Cup finals and, after the withdrawal of Radamel Falcao through injury, took the number 9 shirt for Los Cafeteros.

On 18 July 2015, Sporting CP announced the signing of the Colombia International. Gutiérrez signed a three-year contract with the Lisbon-based club. He scored for Sporting in a 2015–16 Champions League play-off match against CSKA Moscow.

On 26 June 2017, Teo is signed by his hometown’s team Atlético Junior on a three-year deal. He made his debut in a 3–0 victory against La Equidad, scoring the third goal from the penalty spot and overally playing well the whole match. He led his team to a Copa Colombia win in 2017, scoring in the final against Independiente Medellín.

In May 2018 he was named in Colombia’s preliminary 35 man squad for the 2018 World Cup in Russia. However, he did not make the final cut to 23.