Birighitti started his career at the AIS before moving to Adelaide United in 2008. He made his first team debut against Queensland Roar on 17 October 2008 helping Adelaide to a 1–0 win.[2]Aurelio Vidmar praised the young goalkeeper after the match saying "I think Birighitti played well he's got a really good future, he had big shoes to fill and I think he did an outstanding job tonight."[3]
His second successive A-League start came against Perth Glory at Hindmarsh Stadium after Adelaide's number one goalkeeper, 28-year-old Eugene Galekovic, was injured during the Asian Champions League match against FC Bunyodkor.[4] Despite conceding the match's first goal at the near post, Birighitti played his part in the 2–1 win taking Adelaide to the top of the league table.[5]
With Galekovic again ruled out with injury Birighitti started the second leg of the 2008 AFC Champions League Final against Gamba Osaka on 12 November 2008; Adelaide lost the match 2–0.[6] He injured his ankle after falling awkwardly in a training session on 17 December 2008 ruling him out of the remaining A-League 2008-09 season.[7]
Newcastle Jets
On 17 January 2012 it was announced he had signed a two-year contract with A-League club Newcastle Jets starting post the 2012 AFC Champions League group stage.[8]
He quickly became the first choice goalkeeper for the Newcastle Jets, edging out Ben Kennedy and Jack Duncan. In late 2013 he signed a contract extension with the Jets until the end of the 2015–16 season.[9]
On 24 March 2014, Birighitti flew to Germany to discuss a possible transfer to Bundesliga club Bayer Leverkusen.[10][11] After failing to secure a contract with Bayer Leverkusen he then came back to the Jets for the 2014–15 season.
In October 2015, Birighitti was involved in an on-field collision with Sydney FC striker Shane Smeltz. Birightitti suffered multiple broken teeth and required facial surgery after the incident.[12] He returned to action within weeks, missing only one A-League game.[13]
Loan to Varese
On 27 January 2015, Birighitti joined Serie B club Varese on a six-month loan deal.[14] He made his league debut for Varese in a 1–0 away loss to Vicenza on 25 April 2015.[15]
On 1 September 2017, Birighitti joined Eredivisie side NAC Breda on a two-year deal[18] and played the full 90 minutes in NAC Breda's first ever away win in a Eredivisie match against Feyenoord, in which he also stopped a penalty. He departed in the summer of 2018.
Melbourne City
On 11 September 2018, Birighitti joined Australian A-League side Melbourne City on a three-year deal.[19] Playing the majority of the season as understudy to Eugene Galekovic, he negotiated a mutual release from the remainder of his contract.[20]
On 21 July 2022, it was announced that Birighitti had signed a two-year contract with Dundee United, subject to international clearance.[22] He made his first competitive start for his new club in their opening Scottish Premiership match against Kilmarnock which resulted in a 1–1 draw.[23] Birighitti made his European debut in a 1–0 win against AZ Alkmaar,[24] however, the second leg of the tie ended in a 7–0 Dundee United loss, knocking them out the competition.[25]
He went on an emergency seven-day loan to Kilmarnock in January 2024,[26] before being released by Dundee United at the end of the 2023-2024 season when his contract expired.[27]