Baker started the year ranked No. 458, but the world No. 126 will break into the top 100 after his Wimbledon run, with the American likely to enter at about No. 77.
Kohlschreiber goes fourth on the list of the most Grand Slams played before reaching the last eight, having got there on his 33rd attempt.
Fabrice Santoro holds the unenviable record at 54, followed by Australian doubles duo Mark Woodforde on 38 and Todd Woodbridge on 34.
The German made it into the last eight thanks to 23 aces and superb net play.
On Monday afternoon, all at once, there was a frenzy of activity at a wet and windy All England Lawn Tennis Club.
Top seed and 2004 Wimbledon champion Maria Sharapova, a big hitter in her own right, was overpowered in a 6-4, 6-3 loss to No. 15 Sabine Lisicki. while over on Centre Court, there was the not-so-insignificant matter of 16-time Grand Slam champion Federer’s medical timeout to get treatment for his aching back.
The start of the second week has been dubbed “Manic Monday,” because it is the only major tournament that schedules all 16 fourth-round singles matches on one day.
Sure lived up to that moniker this year, even if rain prevented five of the eight men’s matches from finishing.
The most newsworthy result was the abrupt end of Sharapova’s bid to become the first woman since Serena Williams in 2002 to win the French Open and Wimbledon in the same year.
Less than a month after completing a career Grand Slam in Paris to return to world No. 1, Sharapova bowed out against someone she had beaten the three other times they met. She will be replaced atop the rankings next week.
Federer, seeking a seventh trophy at the grass-court Grand Slam, beat Xavier Malisse 7-6 (7/1), 6-1, 4-6, 6-3 to reach a 33rd consecutive major quarter-final, adding to his record.
After the seventh game, Federer got help from a trainer for his back. When he returned, his play did not appear to suffer all that much, other than slower-than-usual serves. On the other hand, Federer capped the match with a 196kph ace.
The Swiss next faces No. 26 Mikhail Youzhny, a 6-3, 5-7, 6-4, 6-7 (5/7), 7-5 winner over Denis Istomin.
Federer is 13-0 against Youzhny, who chose to look on the bright side, saying: “I have one more chance.”
The only other man assured a spot in the quarter-finals was world No. 1 Djokovic.
The defending champion improved to 12-1 against Viktor Troicki, his doubles partner for Serbia at the upcoming London Olympics, by winning 6-3, 6-1, 6-3 under the Centre Court roof.
“Weather is always an obstacle here,” Djokovic said.
Two of the men’s matches never started and three were suspended.
In the men’s doubles, Taiwan’s Lu Yen-hsun and his partner, Germany’s Alexander Waske, bowed out of the tournament after Austria’s Jurgen Melzer and Philipp Petzschner of Germany won their match 6-3, 6-4, 6-7 (6/8), 6-2.
In the women’s singles, World No. 2 Victoria Azarenka, the Australian Open champion, has lost only 14 games so far. The most interesting aspect of her 6-1, 6-0 win over 2008 French Open champion Ana Ivanovic were the pigeon feathers that slowly floated down to the grass after a bird collided with the roof.
“Sometimes it can be annoying when somebody is chewing chips right when you’re serving. Doesn’t really matter; you just have to stay focused on your game. Whatever is going on around, is going on around. It’s out of your hands,” Azarenka said. “But the feathers? It was fun.”