With the snow swirling, Rooney sent the 77th-minute spot kick straight down the middle after Dominic Calvert-Lewin went down following a push in the back by Croatian defender Dejan Lovren.
Mohamed Salah had earlier fired Liverpool ahead with a 42nd-minute stunner that sent the Egyptian clear of Tottenham Hotspur’s England striker Harry Kane as the league’s top marksman with 13 goals this season.
Liverpool stayed fourth with 30 points, 13 adrift of leaders Manchester City who were playing later at second-placed Manchester United. Chelsea are third on 32 with Sam Allardyce’s Everton moving up to 10th.
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