The team from the remote US territory bounced back from last week's 6-0 hammering by Iran in Tehran with a brave display at their National Training Centre ground.
Oman, captained by former Premier League goalkeeper Ali Al Habsi, dominated possession but were unable to break down the hosts.
Guam, with a population of about 165,000, have now won two and drawn one of their home games to lie second in Group D as the fourth round of games gets under way.
Shock wins against Turkmenistan and India -- which has a population of about 1.25 billion -- have put Guam firmly in the mix at the halfway stage.
The 2018 World Cup qualifiers double as a route to the 2019 Asian Cup in the United Arab Emirates, which is expanding from 16 to 24 teams.