The Rainbow Warriors (2-0) overcame a pair of 14-point deficits, scored the game's final 17 points and never led until Meskell's go-ahead kick.
Meskell missed his first three field goal attempts from 48, 27 and 48 yards -- all of them wide left -- before hitting the winner.
Oregon State has lost six in a row dating to last season and have just one win since beating Southern Utah 48-25 on Sept. 8, 2018.
Cole McDonald 30-of-52 passing for 421 yards and Ward finished with 10 catches for 189 yards. The pair hooked up on scoring strikes 29, 35, 5 and 29 yards.
It was the fourth time McDonald went over 400 passing yards in a game and Ward's fourth game eclipsing 100 receiving yards. Ward tied the school record for touchdown receptions in a game.
Oregon State had a chance to tie with 1:25 left, but Jordan Choukair's 52-yard field goal missed wide left. The Beavers eventually got the ball back with four seconds left, but could only get to the Hawaii 45.
Jermar Jefferson carried 31 times for 183 yards and a touchdown and Artavis Pierce added 79 yards and two scores on seven rushes for Oregon State (0-2). Isaiah Hodgins added seven receptions for 96 yards and a touchdown.
Oregon State: The Beavers saw their string of four consecutive wins over Hawaii that dated to 2006 come to an end. It is their first loss to the Rainbow Warriors since the 1999 Oahu Bowl, when head coach Jonathan Smith was the team's starting quarter. Oregon State leads the all-time series 7-4.
Hawaii: The Rainbow Warriors have now beaten two Power 5 teams in the same season for the first time since 2006, when they beat Purdue and Arizona State. They are now 32-61 all-time against current members of the Pac-12. Their last eight wins against a Power 5 team have come against a Pac-12 opponent. It is Hawaii's third straight season with a 2-0 start, which was last achieved from 1980-'82.
Oregon State: Hosts Cal Poly on Sept. 14 in the first meeting between the teams. The Beavers will play three of their next four games at home.
Hawaii: Visits No. 14 Washington on Sept. 14 in its only non-conference road game of the season. The Rainbow Warriors are 2/3 all-time against the Huskies.
Guarantano will deliver in Gator Bowl vs. Indiana
The SEC Now crew believes that Tennessee QB Jarrett Guarantano will have a huge game against Indiana in the TaxSlayer Gator Bowl.
Ohio State's Chase Young wins Nagurski Award
Ohio State defensive end Chase Young won the Bronko Nagurski Award given to the nation's top college defensive player on Monday night.
SEC bowl game predictions
The SEC This Morning crews picks each SEC bowl game.
South Carolina QB Jake Bentley transferring to Utah
South Carolina quarterback Jake Bentley, who started three seasons for the Gamecocks, will transfer to Utah for his final year of eligibility, he announced Monday.
QB Joe Burrow, QB Justin Fields, QB Jalen Hurts, DE Chase Young are finalists for Heisman Trophy
LSU quarterback Joe Burrow, Oklahoma quarterback Jalen Hurts and Ohio State teammates quarterback Justin Fields and defensive end Chase Young are headed to New York this weekend as finalists for the Heisman Trophy.
Kentucky's Lynn Bowden Jr. declares for NFL draft
Lynn Bowden Jr., who took over as Kentucky's quarterback after five games this season when injuries hit the Wildcats hard at the position, announced Monday that he will enter the NFL draft.