The win lifted unbeaten Iran to 14 points, three clear at the top of the Group D standings, with their remaining two fixtures at home to India and Oman in March.
Oman, also undefeated, can draw level with Iran, Asia's highest-ranked team at 43rd in the world rankings, if they beat Turkmenistan away later on Tuesday.
Only the eight group winners and four best runners-up will progress to the third round of Asian World Cup qualifying and also book a spot at the 2019 Asian Cup.
Their previous fixture in Tehran, which Iran won 6-0 in September, was also marked by visa issues for the visiting team, who were eventually granted full entry a day before the match.
Iran had no such luck with four players and two staff unable to accompany the team.
Iran skipper Andranik Teymourian missed his side's 3-1 win over Turkmenistan on Friday to fly to Doha and get a U.S. visa to travel to Guam, Iranian media reported.
Still, Iran were never in trouble against Guam, competing at this stage for the first time and battling with Turkmenistan for third place and the next round of Asian Cup qualifiers. Both have seven points.
Taremi opened the scoring for the visitors in the 12th minute after being slipped through by Mehdi Torabi, who was forced off later in the half because of injury.
Kamyabinia scuffed a right foot shot into the corner of the net for the second in the 32nd minute before three goals in four second half minutes killed the contest.
Rezaeian notched before John Matkin was sent off for hauling down Taremi and substitute Shojaei slotted in the resulting 53rd minute penalty. Ansari Fard then added another against an increasingly disjointed Guam.
Taremi grabbed a second before goalkeeper Alireza Beiranvand was sent off after handling outside the area and taking out Guam striker Shane Malcolm.
Iran defender Ezatollah Pourghaz was forced to play in goal for the last twenty minutes after the visitors had made all their substitutions.
(Writing by Patrick Johnston in Singapore; Editing by Julian Linden)
