Curran scored two of the Spartans' first three goals as San Jose State (11-8) led the entire match and won its third in a row, all over top-20 ranked teams.
Minson kept the Anteaters off the scoreboard until the second quarter with eight saves in the first quarter alone. During San Jose State's current winning streak, the Spartans have allowed just 12 goals and Minson has made 34 saves.
"My defense has been playing really well and I wanted to help them out. It definitely was a team effort," Minson said of the Spartans' defense.
UC Irvine (7-9) closed its deficit to two twice. The last time was 4-2 after a Kat Plummer score with 1:21 left in the third quarter.
Vogt then scored the next three goals in the match, two of them coming in the final minute of the third quarter.
"Dani and Adriana really stepped up from a scoring standpoint. They each had three goals on some pretty good shots. Dani had some nice early shots and Adriana picked it up at the end," said San Jose State coach Lou Tully.
"Minson did a great job. She's a tremendous goalie. Thirteen saves is a lot of saves. She's been doing that consistently and having a great year.
"We're also helping back (on defense) at 2-meters when the ball is put in front of the cage. We want to stop that quickly and we got a lot of field blocks. Those things are huge."
Bridget McKee scored the San Jose State's other goal.
UC Irvine goalkeeper Lauren Davis was credited with three saves in the match.
#13-UC Irvine (7-9) 0-1-1-2=4
#7-San Jose State (11-8) 2-1-3-1=7
UC Irvine - Caitlin Haskell, 2; Kat Plummer, 1; Courtney Collyer, 1.
San Jose State - Dani Curran, 3; Adriana Vogt, 3; Bridget McKee, 1.
UC Irvine - Lauren Davis - 3
San Jose State - Meagan Minson - 12