Venus, 36, is the oldest women’s semi-finalist since Martina Navratilova in 1994 as she also moved a step closer to a final showdown with her sister and defending champion Serena Williams.
The American veteran, seeded eight, enjoyed a 7-6 (7/5), 6-2 victory over Kazakhstan’s world number 96 Yaroslava Shvedova.
German fourth seed Kerber, meanwhile, reached her second Wimbledon semi-final with a 7-5, 7-6 (7/2) win over Simona Halep, the fifth seed from Romania.
Tuesday’s other quarter-finals see six-time champion Serena face Russian 21st seed Anastasia Pavlyuchenkova. Slovak 19th seed Dominika Cibulkova, who is due to get married on Saturday, meets unseeded Elena Vesnina of Russia.
Venus, who won the last of her seven Grand Slam titles at Wimbledon in 2008, is back in the last-four of a Grand Slam for the first time since the 2010 US Open.
Eight-time Wimbledon finalist Venus trails 3-2 in her five career meetings with 28-year-old Kerber, who won their only meeting on grass in the 2012 Olympics at Wimbledon.
“Oh wow, what a tough day on the court. It seemed she was going to win the tie-break but somehow I walked out with the set. She was on fire, but when you can walk to the net as the winner that’s the dream.When you are winning matches it makes it that much sweeter.
I guess if you are Serena Williams it happens a lot, but for Venus Williams this is an awesome day,” she said.