Herbert won the Wimbledon men’s doubles title in 2016 and will partner Britain’s two-time singles champion Andy Murray in this year’s event.
He made his first grass court semi-final against Roger Federer in Halle two weeks ago but the 28-year-old’s deficit was doubled by two sets after Anderson collected a second break.
Anderson broke Herbert’s serve twice more in the third set to wrap up his 19th Wimbledon win on his 40th appearance at a grand slam.
Switzerland’s Stan Wawrinka is also through with a 6-3, 6-2, 6-2 result against Belgium’s Ruben Bemelmans.
Roberto Bautista-Agut of Spain moved into round two after a 6-3, 6-2, 6-3 triumph over Germany’s Peter Gojowczyk.
Djokovic starts his title defence later Monday against another German, Philipp Kohlschreiber.
In the women’s draw, two-time grand slam semi-finalist Madison Keys, the 17th-seeded American, had no trouble in dispatching Thailand’s Luksika Kumkhum 6-3, 6-2.
Another American in Sofia Kenin advanced by defeating Australian Astra Sharma 6-4, 6-2. She will next play Ukraine’s Dayana Yastremska, who bested Italian Camila Giorgi 6-3, 6-3.
Ukrainian eighth seed Elina Svitolina also progressed with ease in a 7-5, 6-0 victory over Australia’s Daria Gavrilova. She goes on to face Margarita Gasparyan following the Russian’s 6-4, 6-4 success over German Anna-Lena Friedsham.
Title holder Naomi Osaka of Japan opens later against Kazakhstan's Yulia Putintseva.
He made his first grass court semi-final against Roger Federer in Halle two weeks ago but the 28-year-old’s deficit was doubled by two sets after Anderson collected a second break.
Anderson broke Herbert’s serve twice more in the third set to wrap up his 19th Wimbledon win on his 40th appearance at a grand slam.
Switzerland’s Stan Wawrinka is also through with a 6-3, 6-2, 6-2 result against Belgium’s Ruben Bemelmans.
Roberto Bautista-Agut of Spain moved into round two after a 6-3, 6-2, 6-3 triumph over Germany’s Peter Gojowczyk.
Djokovic starts his title defence later Monday against another German, Philipp Kohlschreiber.
In the women’s draw, two-time grand slam semi-finalist Madison Keys, the 17th-seeded American, had no trouble in dispatching Thailand’s Luksika Kumkhum 6-3, 6-2.
Another American in Sofia Kenin advanced by defeating Australian Astra Sharma 6-4, 6-2. She will next play Ukraine’s Dayana Yastremska, who bested Italian Camila Giorgi 6-3, 6-3.
Ukrainian eighth seed Elina Svitolina also progressed with ease in a 7-5, 6-0 victory over Australia’s Daria Gavrilova. She goes on to face Margarita Gasparyan following the Russian’s 6-4, 6-4 success over German Anna-Lena Friedsham.
Title holder Naomi Osaka of Japan opens later against Kazakhstan's Yulia Putintseva.