Horvath signed his first professional contract in 2013 with Tippeligaen club Molde in Norway, having been recruited by Molde manager and former Manchester United player Ole Gunnar Solskjær. Horvath first appeared in a Molde matchday squad on August 10, 2013. He made his professional debut on May 16, 2015, replacing Ørjan Nyland in the 55th minute of the match. On July 1, 2015, Nyland was sold to Bundesliga club Ingolstadt 04, leaving Horvath as Molde's starting goalkeeper at age 20. By the conclusion of the 2015 Tippeligaen, Horvath had helped Molde concede just 31 goals for the season, the second-best mark in the league only behind champions Rosenborg. Horvath backstopped Molde to a 5–1 aggregate victory over Pyunik in the second qualifying round of the 2015–16 UEFA Champions League, before a 4–4 aggregate loss on the away goals rule to Dinamo Zagreb in the third qualifying round. Later, in the playoff round of the 2015–16 UEFA Europa League, Horvath and Molde had a 3–3 aggregate win on away goals over Standard Liège. With Molde thus qualifying for Europa League Group A, Horvath joined Brad Friedel, Kasey Keller, Tim Howard, and Brad Guzan as the only American goalkeepers ever to play in the UEFA Europa League/UEFA Cup group stage. On October 2, 2015, Horvath was named to the Europa League Team of the Week, a day after being named Man of the Match for a 1–1 draw against Ajax in which he notched 10 saves, most notably on a point-blank header from Viktor Fischer and on a corner serve from Davy Klaassen in stoppage time. Horvath led Molde to a first-place finish in Europa League Group A with successful two-legged fixtures against Ajax, Celtic, and Fenerbahçe, the latter of which featured two saves on Robin van Persie and three saves on Nani. Combining his play in the Tippeligaen and in the Europa League, he had not allowed multiple goals in a match for over two months. In February 2016, Horvath faced eventual Europa League champions Sevilla in the knockout phase and was unable to prevent a 1–3 aggregate defeat of Molde, although he kept a clean sheet in the second leg.
Club Brugge
On January 3, 2017, Horvath signed with Belgium's Club Brugge on a four-and-a-half year contract. He debuted as Club Brugge's starting goalkeeper on May 5 in the Championship playoffs. After initially letting in a goal due to confusing a whistle from the stands as the referee's whistle, Horvath rebounded to make three saves, and even notched an assist to José Izquierdo off a punt, in a 3–1 victory over Charleroi. The following match, in a 1–1 draw against Anderlecht, Horvath made four saves, including on a penalty kick attempted by Youri Tielemans. Horvath continued to start in goal to close out the season, helping Club Brugge secure a place in the 2017-18 UEFA Champions League third qualifying round. At the start of the 2017–18 season, Horvath resumed his position as the starting goalkeeper for Club Brugge, starting in the first twelve league matches including ten victories. He also started the Champions League qualifying matches against İstanbul Başakşehir and Europa League qualifying matches against AEK Athens, both of which were defeats on aggregate. However, he was eventually benched and then kept out of the squad for much of the season, not receiving another run of starts until May 2018 in the Belgian First Division A Championship Playoffs. He started three matches in the league playoffs as Club Brugge finished as champions and thus qualified for the 2018-19 UEFA Champions League group stage. Horvath began on the bench for Club Brugge in the 2018–19 season behind Croatian international goalkeeper Karlo Letica, but Horvath soon regained the starting job. Horvath posted a trio of consecutive clean sheets against AS Monaco, Borussia Dortmund, and Atlético Madrid in Champions League group stage play while notching eleven total saves. He was named as the goalkeeper for Goal's best XI of the 2018–19 Champions League group stage.
