The duo are challenging for their third Paralympic Games gold medal, after serving up success for the USA at Athens 2004 and Beijing 2008, however Norfolk and Lapthorne will provide tough opposition.
Taylor and Wagner survived a thorough examination by Israel today, edging out Noam Gershony and Shraga Weinberg to triumph 6-3 7-6.
The British pair, meanwhile, had things slightly easier as they saw off Japan's Shota Kawano and Mitsuteru Moroishi 6-2 6-2 .
Two-time men’s Singles medallist Norfolk said confidently: 'We will win the final, I'm happy to play whoever.
'I just think it's so exciting. These are just the best Games ever, it's marvellous.
'The Olympics were sensational, but the Paralympics have just been the wonder of the world so far, and long may it continue.'
Defending women’s Singles champion Esther Vergeer of the Netherlands took only 40 minutes to see off Katharina Kruger 6-0 6-0 and progress to the third round.
Vergeer has now won a remarkable 467 matches in a row, without losing a game in London so far, as she looks to claim a third straight Paralympic Games Singles gold.
She said: 'In the back of my head I'm playing for a gold medal. I trained for this match and I'm prepared for the next.'
Great Britain’s Lucy Shuker defeated Emmy Kaiser with Jiska Griffioen, Yui Kamiji, Aniek Van Koot, Marjolein Buis and Sakhorn Khanthasit all coming through their second-round matches.
Khanthasit was the only player to be pushed into a third set as Daniela Di Toro fought hard to delay a 1-6 6-0 6-3 loss.
The Thai said: 'The weather was really hot, and the light was really bright and the Australian was playing really well. So I felt I really had to play my best.'
Khanthasit went on to enjoy success over Di Toro twice in one day as she later partnered with Ratana Techamaneewat in the women’s Doubles.
Di Toro, with Janel Manns, was on the receiving end of a 6-4 6-0 scoreline on Court One with Germany, Colombia and Republic of Korea’s pairs also progressing to the second round.
The men’s Doubles was also in full swing on Day 5, with Beijing 2008 champions Stephane Houdet and Michael Jeremiasz of France navigating their way to the third round with a comfortable 6-0 6-2 win over Alexander Jewitt and Dave Phillipson.
The pick of the action came on Court Seven, though, as Suwitchai Merngprom and Suthi Khlongrua of Thailand made Japan's Takuya Miki and Takashi Sanada battle all the way for a 7-5 7-5 triumph in a match that lasted just under two hours.