Marshall scored a team-high 25 points despite shooting just 8-17 from the field while Carson added 23 points, six rebounds, and six assists.
The two scored eight of the team's first 11 points of the second half, igniting the crowd of 5,815 as the Sun Devil offense came alive.
ASU stretched its lead to as many as seven before the Beavers (13-9, 5-5) , led by junior guard Roberto Nelson, made a late push to force the overtime period.
Nelson, the Pac-12's leading scoring who entered the night averaging 21.8 ppg, scored 24 of his game-high 26 points in the second half and overtime, including a lay-up with 20 seconds remaining to even the score at 64 and force the extra period as Carson's jumper at the buzzer rimmed out.
Fortunately for ASU, they had enough offensive firepower to prevail late.
The Sun Devils scored 22 points in overtime, including eight from junior Jon Gilling, to hold on for the win.
"We love playing in overtime, I guess," said Bachynski afterwards. "It might not be great for Coach Sendek's blood pressure but it just goes to show you how conditioned we are, how when you put work in in the offseason and it's paying off now."
"It's in these games where we have to play these extra five minutes that you need to be in great shape and I feel like our guys are."
Arizona State shot 48% from the field in the second half and converted 6-9 shot attempts in overtime to escape with the win.
The Sun Devils also forced 15 Oregon State turnovers which led to 19 points and shot 25-40 from the free throw line compared to the Beavers 12-18.
Oregon State entered the game second in the Pac-12, behind only Arizona State, in three-point shooting and used the long ball to stay close in the second half. The Beavers converted 10-16 from deep, including four of five from Nelson.
But the night belonged to Bachynski, who finished with 17 points 15 rebounds, and seven blocked shots in the win; none bigger than his final block of the game with 32 seconds in regulation to prevent a Devon Collier lay-up attempt and help send the game into overtime.
Bachynski entered Thursday just six blocks shy of equaling former Arizona center Anthony Cook on the all-time list and set the tone early with his aggressive demeanor in the post.
On a night when Arizona State struggled shooting the ball, the 7-2 center managed to go 8-12 from the floor, pacing the Sun Devils throughout the game on both ends.
"It's huge," remarked Bachynski of the record. "I'm honored that I can hold that title but you've also got to think about guys in the '60's like Bill Walton. I'm sure he had more blocked shots than I did but they didn't have that stat back then."
"It's because of guys like him that they laid the foundation that I can hold this record and I'm honored to hold it. It's a tribute to those who laid the foundation."
"Anytime I can be a presence at the rim for my team, that's huge. I'm in a system that lets me do that. Coach Sendek changed the whole defense for me so that I can be more at the rim instead of closing out on the wing and I love it."
The Sun Devils return to action on Saturday when they host Oregon at 3:00 pm. They will attempt to complete their second consecutive sweep at home over conference foes and remain in the Pac-12 race.