Johnston told TV's "Inside Edition" he did not tell his former fiancee when the wedding to Oglesby was, but instead just asked her if he could have Tripp for the weekend.
"I wanted him to be my ring bearer," Johnston said of his little boy.
"Inside Edition," which had a correspondent covering the wedding in Wasilla Sunday, said Johnston was a nervous groom and his sweating so profuse, it was reminiscent of Albert Brooks' famous scene in 1987's "Broadcast News."
The program also reported the bridegroom fumbled his vows, which were officiated by his friend, Crosby Marrow.
"Do you take Sunny to have and to hold, from this day forward, for better or for worse?" Marrow asked, to which Johnston responded, "To have and to hold, whatever you say," prompting wedding guests to laugh.
Johnston and Oglesby have a daughter, Breeze Beretta Johnston, who was born last month.
Palin is a former two-time "Dancing with the Stars" contender and the daughter of 2008 Republican vice presidential hopeful Sarah Palin.
Johnston and Bristol Palin, both 22, broke up in 2009, briefly reconciled in 2010, then permanently ended their relationship a short time later.