Both scored touchdowns for Calgary in a 23-18 pre-season win over the B.C. Lions on Tuesday.
Toronto native Derek Wiggan contributed a defensive touchdown for the hosts in front of an announced 25,139 at McMahon Stadium.
Trailing 22-3 after three quarters, the Lions pulled within a touchdown on majors from Josh Harris and R.J. Harris.
On Calgary's 30-yard line with less than 30 seconds remaining, the Lions turned the ball over on downs.
"B.C. rallied on us, but we were able to hold on,'' Stampeder head coach Dave Dickenson said. "Winning is always a good thing.''
Ty Long kicked a field goal for the visitors.
Begelton had a big second half with five catches for 88 yards, including a 41-yard catch and a 27-yard TD reception.
The 23-year-old out of Lamar University needed help off the field in the fourth quarter, however, after he was tackled hard by B.C.'s Adrian James.
Green, a 24-year-old Richmond product, totalled 54 yards in six carries and scored on a 35-yard carry.
"I thought our running back position was very good. That's going to be a tough decision,'' Dickenson said. "I really do like Reggie Begelton. I don't know the injury, what the extent of that was, but he's a guy I think stepped up and showed us what we were seeing in practice.
"That's when you know, kind of when a guy can translate the success in practice and bring it onto the field. A good smart player.''
Dickenson rested quarterback Bo Levi Mitchell because of competition between Canadian Andrew Buckley, Mitchell Gale and former NFL prospect Ricky Stanzi for the open backup job.
The coach wanted to give the three men ample time to compete for it.
Buckley completed 6-of-8 passes for 59 yards. The former University of Calgary star rushed for 20 yards and was sacked three times before he was replaced in the second quarter by Gale.
The 27-year-old, who has spent time in the Saskatchewan, Hamilton and Toronto organizations, was 5 for 9 in passing for 87 yards and a touchdown pass. Stanzi went 8 for 12 for 87 yards in the fourth quarter.
"Quarterback play was very solid until about the fourth quarter. Rick, unfortunately, we were breaking down up front,'' Dickenson said. "We started from the one-yard line twice. Tough to have a lot of success there.
"We'll hopefully give him a little bit more work next week.''
All four B.C. quarterbacks saw action, including starter Jonathon Jennings who completed 3-of-8 passes for 28 yards.
Keith Price was 9 for 12 in passing for 49 yards, plus another eight yards on two carries. Veteran Travis Lulay played the third quarter completing four of five passes for 31 yards.
Alex Ross ran cold then hot in the fourth quarter.
The 24-year-old was picked off throwing the ball into the end zone, but then compiled 134 passing yards and threw a touchdown pass to R.J. Harris to give B.C. a chance to win.
"The rebound was good,'' Lions coach Wally Buono said. "He showed he's got the ability to execute under pressure and use his legs like I thought he would.''
Precision punting by Calgary's Rob Maver in the first half had B.C.'s offence starting within seven yards of their goal line four times. Maver missed a pair of field-goal attempts in the game, however.
Calgary's Jameer Thurman stripped Price of the ball, which rolled into the end zone for Wiggan to fall on for a major late in the second quarter.
Calgary plays again Sunday in the tightest turnaround of the pre-season for any CFL team. The Stampeders are in Edmonton to face the Eskimos.
"I worked them quite hard in training camp,'' Dickenson said. "Because we have the two games in the first week, I'm not going to get a ton of work these next five days.''
The Lions are at home to the Saskatchewan Roughriders on June 16 to conclude their pre-season.
Calgary's season-opener is June 23 against the host Ottawa Redblacks in a Grey Cup rematch. The Lions are home to the Eskimos the following day for their respective season-openers.