Favourites Germany, who were runners-up to Switzerland past year, were worked hard in two three-set singles matches, before completing a fine day's work 4-2 4-3 (5-3) in the doubles.
The 20-time Grand Slam singles champion broke immediately in the second set and looked sharp as he cruised to an easy first-up victory in the tournament.
"I am happy in all aspects of my game that things were working - foot work, offensive play, serve, return - it was all there".
"It was very good".
"It's nice that I'm feeling as good as I am and I played a wonderful match against Cameron".
World No 91 Norrie, who had defeated Greek Stefanos Tsitsipas in straight sets on Saturday for the biggest win of his career, struggled to match Federer's crisp stroke-making as the Swiss gave his team a 1-0 lead.
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The four singles matches in Perth were part of a 21-match winning streak to start the year, including a second successive Australian Open title in Melbourne.
Veteran Roger Federer claimed a commanding 6-1, 6-1 victory over 23-year-old Cameron Norrie to earn Switzerland a first point.
Roger Federer of Switzerland gestures to the spectators before hitting signed tennis balls into the stands during day two of the 2019 Hopman Cup at RAC Arena on December 30, 2018 in Perth, Australia.
The famously unflappable Swiss acknowledges being excited about the prospect of taking on his fellow tennis great on Tuesday in a Hopman Cup mixed doubles match between Switzerland and the United States.
Hoping for a similar start to the new season under new coach Rainer Schuttler, Kerber took the first set against Muguruza comfortably in the battle of the two former world number ones.
A break of serve in the fourth game of the third set was enough to ensure Kerber maintained her flawless record in Perth, winning 6-2, 3-6, 6-3.
Although Zverev is ranked fourth in the world and Ferrer 126th, the German said he expected nothing less from the Spaniard, who who retired from Grand Slam tennis.