The Jets scored six unanswered goals after falling behind 2-1 in the first period when Alex Chiasson and Tyler Seguin scored in a 37-second span for Dallas.
Jokinen and Enstrom added two assists each and Blake Wheeler had four helpers.
"These guys battled for me," said Montoya. "This is what they pay me for. I've been waiting for this chance."
The Jets scored their first four goals on 17 shots against Tim Thomas, who was pulled after 20 1/2 minutes. Cristopher Nilstorp gave up three goals on 17 shots after that for the Stars, who had a four-game point streak snapped (3-0-1).