Dickson scored 11 seconds into overtime with the only shot taken in the extra session to give the Roughnecks a thrilling victory.
Dickson also scored twice within a 30-second span late in the fourth quarter to give Calgary (7-5) an 11-10 lead. Sean Pollock forced overtime for Colorado when he scored with 37.9 second left in the fourth.
Calgary is now tied with the Washington Stealth and Edmonton Rush for the lead in the NLL's West Division.
Shawn Evans had three goals and seven assists for the Roughnecks. Dane Dobbie had a pair of goals, while Geoff Snider, Scott Ranger and Jeff Shattler scored as well.
Pollock had a hat trick for Colorado (4-8), while Jordan McBride had two goals and five assists. John Grant had three goals and three assists for the Mammoth.
Grant, from Peterborough, Ont., is now three points away from passing Victoria's Gary Gait for third all-time in NLL scoring. Grant has 1,163 points to Gait's 1,165.
Adam Jones, Jamie Lincoln and Creighton Reid also scored for the Mammoth.
The Roughnecks dug a huge hole in the first half because of penalties. Colorado had four power-play goals took a 7-3 advantage into the third quarter.
Colorado was 5 for 6 on the power play for the game and Calgary 5 for 7.
Both offences had plenty of chances in the first half, but Colorado's goalie Tye Belanger was solid, blocking 18 shots.
Grant scored on three of his four shots in the half, two of them on the power play, and Colorado exploded for a five-goal second quarter.
A five-minute roughing call on Colorado's Rory Smith late in the second quarter set the Roughnecks up for three power-play goals that got them back in the game at 8-6. Colorado led 9-6 heading to the fourth quarter.
Calgary started well, with Dobbie scoring on the power play 2:50 into the contest but the Mammoth got untracked and took a 2-1 lead after 15 minutes.
Calgary outshot Colorado 51-43.
NOTES — Attendance was 9,493. . . Mammoth defenceman Rory Smith has played 81 NLL contests without scoring a goal . . . Evans reached 200 goals for his career with his second goal of the night . . . The Roughnecks prepare for a key home-and-home series with the Washington Stealth with games next Saturday and in Calgary April 6 . . . The Mammoth return home to Denver to face the Philadelphia Wings next Saturday.