Born in Seville, Andalusia, Pozuelo spent his youth career at his local club Real Betis. He made his senior debut with the B-team, spending two seasons in Segunda División B. Pozuelo made his official debut with the main squad on 2 October 2011, playing the second half of a 0–1 La Liga home loss against Levante UD. On 18 December he scored his first league goal for the Verdiblancos, as well as being sent off in the 2–0 win at Atlético Madrid. Pozuelo was promoted to Betis' first team for the 2012–13 campaign. He appeared in a total of 13 games in all competitions, netting his only goal in a 5–3 away success over Athletic Bilbao. In total, Pozuelo made 33 appearances during his tenure, scoring three goals across all competitions.
Swansea City
On 2 July 2013, Pozuelo joined Swansea City on a three-year contract for an undisclosed fee, signing alongside teammate José Cañas and becoming the seventh Spaniard in the squad. He scored on his debut for the club, rounding off the scoring in a 4–0 home victory over Malmö FF in the first leg of the third qualifying round of the UEFA Europa League; he netted his second in the same competition and also at the Liberty Stadium on 22 August 2013 in a 5–1 play-off round win against Romania's FC Petrolul Ploiești. During his spell in Wales, Pozuelo played 36 matches across all competitions, scoring twice and adding six assists.
Rayo Vallecano
Pozuelo returned to his country's top division on 24 July 2014, joining Rayo Vallecano for an undisclosed fee. His first competitive appearance took place on 14 September, as he came on as a 61st-minute substitute in a 2–3 home loss to Elche CF. Pozuelo took part in 13 official games during his only season, registering one goal in the Copa del Rey against Valencia CF.
Genk
On 31 August 2015, Pozuelo moved abroad again, signing a two-year deal at Belgian First Division A team K.R.C. Genk. He scored six goals in 2016–17, helping to a final eighth position in the regular season; he later became their captain, and collected a total of 175 appearances across all competitions over five seasons, with 25 goals and 60 decisive passes. In February 2019, Toronto FC planned to trigger Pozuelo's €8 million release clause, however, a disagreement ensued with Genk questioning the validity of the release clause and refusing to allow the player to move. Following a lengthy transfer discussion, the two sides reached a compromise for the player to finish out the main portion of the season with the latter and join the former on 18 March. When he left, Genk were sitting in first place in the domestic league.
A diminutive, versatile, hard-working and creative midfielder, with good ball skills, technique and an eye for goal, Pozuelo usually plays in a playmaking role as an attacking midfielder, although he is also capable of playing as a central midfielder. Although naturally right-footed, he is capable of playing off of either foot, and is known for his vision and ability to provide assists for teammates. Toronto FC president Bill Manning described him as "a guy who can pull the strings, someone who can manage the game, make the special plays that make goals", while the club's manager Greg Vanney described him as "an attacking player first and foremost. We want to use him in that role. He’ll play close to and we’ll use him a lot in setting up our attacks. He's outstanding at understanding how to move around, manipulate numbers on the field, play between lines. the vision for the final pass and the ability to spring some of our guys as runners. But it’s also his ability to finish plays off in different ways. For us it’s the engine through that final phase of our attack.” Pozuelo has also been used as a false-nine on occasion.
