In the first fixture of the season, Palacio scored a brace against Cittadella in the third round of the Coppa Italia.

He also scored in the first league game of the season, against Genoa on 25 August; his goal came in injury time, giving Inter a 2–0 win, which was followed by another goal and an assist in a 3–0 win against Catania.
On 20 October, Palacio scored twice to give Inter a 3–3 draw against Torino at the Stadio Olimpico, and six days later scored in a 4–2 triumph against recently promoted Hellas Verona at San Siro.
On 3 November, Palacio continued his fine form, scoring a header and assisting in a 0–3 away win against Udinese at the Stadio Friuli.
On 22 December, he scored a superb goal in the 86th minute with the back of his heel after an assist from Fredy Guarín, which proved to be decisive with Inter winning 1–0 against Milan.
That was his first competitive goal in the Derby della Madonnina.
Thanks to his goal, Inter ended 2013 with a win and situated in fifth place with 31 points.

On 15 February 2014, Palacio scored his first goal of 2014 after some negative displays during the 2–1 away win against Fiorentina.
On 9 March, he scored the winning goal against Torino at the San Siro, giving Nerazzurri three important points.
Five days later, Palacio signed a new two-and-a-half year contract with Inter which will keep him at the club until 2016.
One day after he extended his contract, Palacio scored the opening goal and assisting the winner of Jonathan in the 2–0 away win against Hellas Verona.
Palacio continued with his good appearances by scoring his 15th league goal in the 4–0 thrashing of Sampdoria at the Stadio Luigi Ferraris.
He also assisted both goals from Mauro Icardi.

On 10 May, in Javier Zanetti's last competitive match at the San Siro in which Inter defeated Lazio 4–1 to secure a place in Europa League play-off for next season, Palacio scored a brace and in both occasions went to celebrate with Zanetti.
He was first assisted by Mateo Kovačić and later by Yuto Nagatomo.
Palacio ended the 2013–14 season with 39 appearances (37 in Serie A) and 19 goals (17 in Serie A), finishing as Inter's top goalscorer.
In the first fixture of the season, Palacio scored a brace against Cittadella in the third round of the Coppa Italia.
He also scored in the first league game of the season, against Genoa on 25 August; his goal came in injury time, giving Inter a 2–0 win, which was followed by another goal and an assist in a 3–0 win against Catania. On 20 October, Palacio scored twice to give Inter a 3–3 draw against Torino at the Stadio Olimpico, and six days later scored in a 4–2 triumph against recently promoted Hellas Verona at San Siro. On 3 November, Palacio continued his fine form, scoring a header and assisting in a 0–3 away win against Udinese at the Stadio Friuli. On 22 December, he scored a superb goal in the 86th minute with the back of his heel after an assist from Fredy Guarín, which proved to be decisive with Inter winning 1–0 against Milan. That was his first competitive goal in the Derby della Madonnina. Thanks to his goal, Inter ended 2013 with a win and situated in fifth place with 31 points.
On 15 February 2014, Palacio scored his first goal of 2014 after some negative displays during the 2–1 away win against Fiorentina. On 9 March, he scored the winning goal against Torino at the San Siro, giving Nerazzurri three important points. Five days later, Palacio signed a new two-and-a-half year contract with Inter which will keep him at the club until 2016. One day after he extended his contract, Palacio scored the opening goal and assisting the winner of Jonathan in the 2–0 away win against Hellas Verona. Palacio continued with his good appearances by scoring his 15th league goal in the 4–0 thrashing of Sampdoria at the Stadio Luigi Ferraris. He also assisted both goals from Mauro Icardi.
On 10 May, in Javier Zanetti's last competitive match at the San Siro in which Inter defeated Lazio 4–1 to secure a place in Europa League play-off for next season, Palacio scored a brace and in both occasions went to celebrate with Zanetti. He was first assisted by Mateo Kovačić and later by Yuto Nagatomo. Palacio ended the 2013–14 season with 39 appearances (37 in Serie A) and 19 goals (17 in Serie A), finishing as Inter's top goalscorer.
Rodrigo Palacio