Footage of the pair was captured by a home camera in their bedroom and shows one toddler crying on the floor while his brother worked out the best way to get him out.
Their dad, Ricky Schoff, from Utah, US, shared the video on Facebook to warn parents to secure furniture to the wall.
“I’ve been a little hesitant to post this,” Schoff wrote on Sunday 1 January. “But I feel it’s not only to bring awareness, but it is also incredible.
“We are so grateful for the bond that these twin brothers share. Please make sure all your dressers are bolted and secured to the wall. Please share.”
The video, originally posted to YouTube on 31 January, shows the toddlers initially trying to climb in the open, empty drawers before the cabinet fell over.
While the toddler who was stuck tried to wriggle free, his brother walked around the chest of drawers trying to work out how to move it, before managing to push it successfully.
“One smart and brave brother,” one person commented on the video. “This is sad to watch but a good reminder of how dangerous these drawers can be.”