Newly promoted Brighton made a positive start to their inaugural Premier League season, sitting in 8th place after eleven games. An unbeaten run of four games from mid-October coincided with Murray hitting a good run of form, with the striker scoring four goals in the three games preceding the November international break. His scoring run began with two against West Ham United in a 3–0 away win, and he followed it up with goals against Southampton at home and Swansea City away, earning Brighton four points. On 8 January 2018, Murray scored the winning goal in Brighton's 2–1 victory over arch rivals and former club Crystal Palace to eliminate them from the FA Cup at the third-round stage.
On 1 September 2018 Murray scored twice to take Brighton from 2–0 down to draw 2–2 with Fulham. His 100th goal for Albion, the only goal of the match at home to Wolverhampton Wanderers on 27 October, made him just the second man – after Tommy Cook with 123 – to reach that milestone. Murray signed a one-year contract extension on 13 November that runs to the summer of 2020. After 9 games without scoring, on 29 January 2019 Murray scored another two goals against Fulham in a 4–2 away defeat. This time Fulham came back from 2 goals behind, and won. On 6 February 2019 Murray scored another two goals this time coming off the bench in a fourth round FA Cup replay against West Brom where his goals put Brighton 2–1 and 3–1 up in the 3–1 victory. On 9 March 2019 Murray scored his 100th league goal for The Seagulls at his former club and bitter rivals Crystal Palace in a 2–1 away victory. This win meant Brighton won the double over Palace.
On 24 January 2018, Murray and his wife Stacey were arrested on suspicion of tax fraud totalling £1.1 million. In April 2019, HMRC announced that they had concluded their criminal investigation and no charges had been brought.