Anderson was a convincing 6-3 6-4 winner over Russian Evgeny Donskoy in their second-round clash on the Washington hard courts.
The South African seventh seed next faces Malek Jaziri after the Tunisian upset Czech 11th seed Radek Stepanek 2-6 7-6 (7-3) 6-1.
Anderson may have taken just 79 minutes to advance, but ninth seed Karlovic needed two hours 25 minutes.
The big-serving Croatian sent down 24 aces as he battled past Frenchman Benoit Paire 7-6 (7-5) 6-7 (11-13) 7-6 (7-2).
Paire saved five match points in the second-set tie-break before the in-form Karlovic recovered to win the deciding set.
Lu Yen-hsun, the 16th seed from Chinese Taipei, was well beaten by Slovakian Lukas Lacko, who completed a 6-1 6-4 victory.
Other second-round winners included Lleyton Hewitt, Denis Istomin and Tim Smyczek.
Veteran 14th seed Hewitt was too good for Australian countryman Marinko Matosevic 6-4 6-3, while Uzbek 15th seed Istomin powered past Bernard Tomic 6-4 7-6 (8-6).
American Smyczek upset French 12th seed Jeremy Chardy 7-6 (7-5) 3-6 6-4.
In first-round matches at the ATP 500 event, there were no major upsets on Tuesday.
American Jack Sock, runner-up in Atlanta on Sunday, beat German Michael Berrer 7-6 (7-2) 6-4.
Australian lucky loser Sam Groth served 16 aces but was beaten 7-6 (7-3) 3-6 6-4 by Israeli Dudi Sela.
Germany's Benjamin Becker claimed a 6-3 7-6 (9-7) win over Slovenian Blaz Kavcic, American Sam Querrey proved too much for countryman Michael Russell in a 6-4 6-3 victory and Steve Johnson got past Australian wildcard James Duckworth 6-3 7-6 (7-4).
Veteran Victor Estrella Burgos of the Dominican Republic battled past German Tobias Kamke 6-2 4-6 7-6 (7-4).