Things had threatened to turn ugly for the 111th-ranked Kudla when he lost the first five games, but he fought his corner to ensure the score stayed respectable and the match remained competitive.
The holder and four times champion allowed a few match points to go begging before finally wrapping up victory in an hour and 33 minutes to set up an encounter with Poland's 48th-ranked Hubert Hurkacz.
At this stage of the tournament, few would bet against Djokovic winning a 16th Grand Slam title next Sunday and the world number one certainly sounds confident.
Reilly Opelka blasted his way into the third round at Wimbledon, coming through 7-5 3-6 4-6 6-4 8-6 against the 22nd seeded Stan Wawrinka for the biggest win of his career.
Karen Khachanov and Daniil Medvedev continued Russian advance at Wimbledon, beating Feliciano Lopez 4-6 6-4 7-5 6-4 and Australia's Alexei Popyrin 6-7(6) 6-1 6-4 6-4, respectively, to progress into the third round.
On the women’s side, former world number ones Simona Halep and Victoria Azarenka have set up a third-round showdown after defeating Romania’s Mihaela Buzarnescu 6-3 4-6 6-2 and Australian Ajla Tomljanovic 6-2 6-0, respectively, on July 3.
