World number 22 Kerber rolled back the years with a battling 6-2 4-6 6-4 victory in a time of a little over two hours on Thursday.
She converted four of her nine break points and will now face the unseeded Oceane Dodin, who needed just an hour to overcome Viktorija Golubic 6-3 6-0.
Top seed Karolina Pliskova continued her progression with a 6-4 7-6 (8-6) victory over Maryna Zanevska, meanwhile, and will take on Kaja Juvan for a place in the final after she beat fourth seed Elise Mertens 7-6 (7-3) 6-4.
Pliskova, who saved four set points in the tie-break, is aiming to become the fourth Czech champion in Strasbourg.
At the Grand Prix Sar La Princesse Lalla Meryem, Anna Bondar is the last seed standing after opponent Ajla Tomljanovic retired injured when 5-1 down in the opener.
Clair Liu saw off Astra Sharma 6-4 6-1 to reach the semi-finals in Morocco, while Lucia Bronzetti and Martina Trevisan will meet in the other final-four showdown.
Bronzetti outlasted third seed Nuria Parrizas-Diaz 6-1 3-6 7-6 (7-5) while Liu beat Astra Sharma 6-4 6-1.
Having endured an injury-hit season to date, world number eight Pliskova made the perfect start to her campaign in France with a routine 6-4 6-2 win over Ukrainian 19-year-old Marta Kostyuk.
Kerber, who is only missing a victory at the French Open – which begins later this month – to complete a Career Grand Slam, overcame teenager Diane Parry 6-3 6-4 in her opener, setting up a round-of-16 clash with world number 45 Aliaksandra Sasnovich.
Some of the other big names participating in Strasbourg, however, were not so lucky, with 5th and 6th seeds Shuai Zhang and Sloane Stephens crashing to first-round exits.
Shuai went down 6-2 6-3 to Belgium's Maryna Zanevska and Stephens capitulated to a 2-6 6-4 6-1 loss to Nefisa Berberovic, while Heather Watson set up a last-16 meeting with eighth seed Magda Linette by beating Katharina Hobgarski 6-4 6-1.
Meanwhile, Garbine Muguruza made a winning start to her campaign at the Grand Prix Sar La Princesse Lalla Meryem in Morocco, as the world number 10 builds towards a tilt at French Open glory having triumphed at Roland Garros back in 2016.
Muguruza had few difficulties in beating Anna Danilina 6-3 6-2, and will face Martina Trevisan in the round-of-16 after the Italian beat China's You Xiadoi 6-0 6-4.
Third seed Nuria Parrizas-Diaz had to come through a more difficult challenge in Rabat, overcoming Carol Zhao 7-6 (7-4) 1-6 6-2, while eighth seed Anna Kalinskaya was the highest-ranked player to fall at the first hurdle, going down 6-3 6-7 (5-7) 6-3 to Lucia Bronzetti.
Second seed Tomljanovic wrapped up a 6-2 6-1 win over her Spanish opponent in Rabat on Sunday, kick-starting her bid to better her second-placed finish at the 2018 edition of the event.
The world number 44, who was beaten by fellow Australian Ashleigh Barty in the Wimbledon quarter-finals after overcoming Emma Raducanu in London last year, is on course for a potential meeting with Croatian 16-year-old Petra Marcinko, who shocked ninth seed Rebecca Peterson to claim a three-set victory.
The Australian Open girls' champion and junior world number one claimed a superb 6-0 2-6 7-5 win over the Swede for her first career top 100 triumph.
At the Internationaux de Strasbourg, meanwhile, eighth seed Linette saw off Varvara Gracheva 6-3 6-0 to reach the round-of-16, setting up a potential tie with Heather Watson.
Elsewhere, Harmony Tan downed Australia's Samantha Stosur 6-2 6-1 to set up a potential round-of-16 meeting with Shuai Zhang, who faces Belgium's Maryna Zanevska on Monday.
Second seed Tomljanovic was a 7-5 6-2 victor against Anna Karolina Schmiedlova, reeling off the last four games in succession to advance in Morocco.
Fellow Australian Astra Sharma joined her in the last eight by overcoming wildcard Petra Marcinko 5-7 6-3 6-3.
Kristina Mladenovic had to save a match point after passing up two herself to finally get over the line with a 6-3 3-6 7-6 (9-7) success - her first singles win of the year - over lucky loser Tessah Andrianjafitrimo in a first-round clash.
At the Internationaux de Strasbourg, third seed Cirstea stormed to a one-set advantage against Ekaterina Makarova but soon fell away and succumbed to a 1-6 6-3 6-2 loss.
Magda Linette breezed past Heather Watson 6-1 6-1 to reach the quarter-finals, where she was joined by Maryna Zanevska after the Belgian's 4-6 7-5 6-1 comeback win against Harmony Tan.
Top seed Karolina Pliskova awaits American Bernarda Pera who defeated Elena-Gabriela Ruse in straight sets, while Anna-Lena Friedsam will take on Elise Mertens after rallying to beat Daria Saville 4-6 6-3 7-6 (7-5).
