Everton had offered next to no attacking threat in a game they were second best in for large periods but Rooney slammed home from the spot with 14 minutes left after Dejan Lovren had bundled Dominic Calvert-Lewin over in the box, a decision furiously protested by the Liverpool defender.
Mohamed Salah had earlier given Jurgen Klopp’s side a deserved lead to continue his sensational season.
The winger curled home a wonderful effort from 15 yards in the 42nd minute to take him above Harry Kane as the Premier League’s outright top scorer this season.
But Salah missed a golden opportunity to put the game to bed with a back-post header shortly after the break and the Toffees took full advantage of that reprieve to maintain Sam Allardyce’s unbeaten start to life at the club.
Klopp made the surprise decision to name Roberto Firmino and Philippe Coutinho on the substitutes’ bench, but the Brazilian duo’s absence was hardly felt in the early stages with Sadio Mane, James Milner and Salah all seeing shots deflected or blocked by a stretched Everton backline.
Allardyce’s side soon found their defensive shape, however, and largely reduced the Reds to efforts from distance as the first half wore on.
Salah had been well shackled by Cuco Martina in a strangely subdued appearance, but he spectacularly got the better of the Toffees left-back as the interval approached.
The Egypt international showed superb strength to shrug off Martina before waltzing past the challenge of Idrissa Gueye and curling in a wonderful strike into Jordan Pickford’s top right-hand corner for his 13th league goal of the season.