Ola Toivonen's first-half penalty secured a 1-0 home win for Victory against Thai debutants Chiangrai United, while Ulsan Hyundai and FC Tokyo drew 1-1.
The Group E games between Beijing Guoan and FC Seoul, and Shanghai Shenhua against Perth Glory in Group F, have both been postponed until April because of travel restrictions aimed at halting the coronavirus.
A swathe of countries have barred arrivals from China to fight the outbreak, which has killed more than 1,000 people in China and infected more than 42,000 in 25 countries.
Most Champions League games involving Chinese clubs have been put on hold for two months, extending the group stage and shunting the East zone's round of 16 back to June 16-24.
Also on Tuesday, Asia's second-tier AFC Cup postponed its East zone games until April, affecting teams from Taiwan, Hong Kong, Macau and Mongolia.
Victory's 1-0 win was far from convincing against Thai champions Chiangrai, who had a man sent off late on as their tournament debut ended on a sour note.
But it was welcome for Carlos Salvachua's side, who have won just four of their 17 A-League fixtures this season to sit third from bottom on the 11-team domestic table.
"They made us work for it," said Toivonen. "We controlled the first half but we were a little bit anxious in the second. But it's always important to get a good start in the group."
Victory have only once advanced beyond the group stages in seven previous campaigns -- when they were eliminated in the round of 16 under then coach Kevin Muscat.
After a slow opening period at AAMI Stadium in Melbourne, Victory began pressing and Toivonen's curling shot was well saved after 22 minutes.
The deadlock was broken three minutes later when Toivonen was pulled down off the ball in the box and the Swedish striker stepped up to convert the penalty.
Despite the match being largely played in the Chiangrai half, few other chances were created against a stubborn opposition.
However, Chiangrai's night ended badly with Thirayu Banhan sent off in the dying minutes for a dangerous tackle.
In the later kick-off in Ulsan, the hosts had FC Tokyo's Adailton to thank as he headed a late own goal to leave the scores all square at 1-1.
Ulsan striker Bjorn Johnsen smashed a volley against the bar early on, and had a fierce shot tipped over nine minutes into the second half.
Diego Oliveira put FC Tokyo ahead with a neat finish on 64 minutes but with eight minutes to go, Adailton gifted Ulsan a point when he headed past his own goalkeeper from a hanging free-kick.