Winners of their first five league games for the first time since 1990, Liverpool returned from the international break to blank a lethargic Tottenham side that have failed to capitalise on the emotion of their 3-0 win at Manchester United on Aug. 27.
Firmino nearly set the tone after 45 seconds with a goal that was disallowed when Sadio Mane was ruled to be offside, and though Michel Vorm parried away an attempt by Mohamed Salah after 22 minutes, Liverpool struck first behind Wijnaldum.
Vorm, again replacing the injured Hugo Lloris, punched away James Milner's corner and Eric Dier headed it clear, but Wijnaldum scored from a header in the 39th minute after Vorm caught it behind the goal line.
It was the first away Premier League goal for Wijnaldum and it was confirmed by goal-line technology, with referee Michael Oliver pointing to his wrist amid objections by Tottenham players.
Mane nearly doubled the lead in the 49th minute before Vorm turned his attempt away, and Lucas Moura almost equalised for Tottenham after his shot hit the left side of the net, but Liverpool increased their advantage in the 54th minute on Firmino's simple strike.
Vorm failed to control the rebound after Mane's cross from the right was turned onto the post by Jan Vertonghen, and Firmino collected himself to poke it over the goal line for his second league goal of the season and second in as many games.
Harry Kane failed to connect with Kieran Tripper on a cross in the 66th minute, and Erik Lamela's attempt in the 85th minute went wide for Spurs, who appeared to get a lift once Son Heung-Min came on in the 73rd minute for his first appearance since winning the gold medal for South Korea in the Asian Games earlier this month.
Lamela pulled one back in added time for Spurs, who were supposed to open their new stadium with the game before it was pushed back by construction delays.