Tsonga started like an express train, forcing break opportunities at will (he took two of eight) as Kohlscreiber battled on serve. The second set was much closer but Tsonga was good enough to hold onto his initial break and close out the set. He'll play Fabio Fognini tonight, in a clash that could be a match for the ages, given the flair of the two Europeans.
Tsonga's win meant six of the eight seeds progressed, with only fifth seed Benoit Paire falling by the wayside.
David Ferrer began his 2016 campaign here with an efficient 6-2, 6-4 second round victory over Australian qualifier Matthew Barton.
It was his 33rd match in Auckland; surely no one in the modern era has played more.
When Ferrer played here for the first time, John Key was an unknown MP for Helensville, John Mitchell was coach of the All Blacks and Marina Erakovic was an aspiring junior at the city's Kohimarama Tennis Club.
That was in January 2003 and the 21-year-old Ferrer arrived as world No58.
"I remember when I played my first time here," said Ferrer.
"It was another generation - it was all new for me, a new goal. Now I am more comfortable, positive [calmer]. In 2003, I was more inconsistent."
Since then Ferrer has lifted the trophy here four times, and reached the semifinals twice.
Ferrer was happy with his work against Barton, who showed plenty of pluck - at one stage diving for a volley like he was at Wimbledon - but never really troubled the Spaniard.
"It was a good match for the first round," said Ferrer.
"The court was fast and it is never easy. But I played consistent and without too many mistakes."
Today, Ferrer faces Czech Lukas Rosol, who trumped a tired looking Paire 6-4, 7-6 (5).
2.08m John Isner outlasted 1.98m Sam Querrey 7-6 (8) 6-7 (4) 6-4, in a forgettable snore fest where the rallies were as short as the players are tall.
Fourth seed Kevin Anderson made a strong start, with a 7-6 (10-8), 7-6 (5) win over resilient Dutchman Robin Haase.
"It was a tricky, tough match," said Anderson. "But I had much better rhythm by the end."
Other second round winners included sixth seeded Spaniard Roberto Bautista Agut, Jack Sock and Fabio Fognini.
The local highlight was Michael Venus and Croatian partner Mate Pavic progressing through to the quarter-finals of the doubles, with a 6-4, 6-2 victory over Chris Guccione and Andre Sa.
However, fellow Kiwis Wesley Whitehouse and Finn Tearney lost 7-5 6-2 to American duo Donald Young and Nicholas Monroe.