The Wildcats were able to hang on in overtime 68-62 and improve to 3-0 on the season.
"Marlies (Gipson) was heads-up on the in-bounds play and she hit me and I wasn't really guarded that tight so I just threw up a shot and it went in," said Coggins, who scored 13 points and grabbed six rebounds.
"So I'm really happy the one three that I did make came at a really good opportune time."
An opportune time is an understatement. With 1.3 seconds left on clock and the score tied at 52, Wyoming's Justyna Podziemksa got a great look from behind the 3-point line and hit it.
"We talked about playing for 40 minutes," said Wyoming coach Joe Legerski, who dropped to his knees when Coggins' shot sank. "I thought we played 39 minutes and 58 seconds, but we still have to try to get a hand up."
Kansas State carried that momentum into the five minutes of bonus ball and played with an energy that had really been lacking for most of the game.
Off of the tip, sophomore guard Kimberly Dietz hit a quick jumper to put the Cats up by two, but Wyoming guard Jodi Bolerjack came right back down the court and made her fourth consecutive 3-pointer.
That basket turned out to be the Cowgirls' final field goal of the night as the Wildcats scored on their next three possessions, including a turnaround 3-pointer by sophomore forward Marlies Gipson with two seconds left on the shot-clock.
And while the headlines belong to Coggins today, the story for K-State is junior forward Shana Wheeler.
Wheeler played her best game as a Wildcat since suffering a season-ending torn ACL injury nearly a year ago. Coming off the bench in her first game without the knee brace, the Lee's Summit, Mo., native led Kansas State with career-highs of 16 points and six blocks, in addition to grabbing seven rebounds.
"I thought it was a real break-out game for Shana," K-State coach Deb Patterson said.
"Defensively I thought she completely changed the game, both with her blocks and her switches, and her ability to go get boards. And I think it's just a sign of what we will see as she continues to have the opportunity to get back the feel for playing."
The Wildcats set a single-game record for most blocks in a game with 13. Gipson tied her career-high with five. And Wheeler joins two efforts by Nicole Ohlde ('02 and '04) for the third-most blocks in a game.
Kansas State led the entire first half, jumping out to a 12-point lead after shooting 52-percent from the field, but for the second game in a row they cooled down quickly. Wyoming (2-1) closed the gap to three at intermission and took the lead, 35-34, during an 11-4 run early in the second half.
The Cowgirls' largest lead of the night was six points with 13:24 left in regulation and at that point K-State finally made some adjustments and picked up its defensive intensity. The lead changed two more times before Coggins' half-court Hail-Mary.
Wyoming forward Hanna Zavecz led all scorers with 19 points on 6-for-11 from the field.
Gipson recorded her fifth career double-double with 14 points and 11 boards.