Both goals for Jooris came in the third period. The first, at 4:03, put the Flames ahead for good at 2-1.
Most of the work on the goal came from Johnny Gaudreau, who spun away from a Jets defenceman along the boards, than drew the other defenceman towards him before slipping the puck to a wide open Jooris.
Monahan made it 3-1 just 40 seconds later, and Jooris scored his second goal at 9:05, again on a nice set-up from another Calgary rookie, Sam Bennett. Gaudreau started the sequence with a nice chip along the boards, and Bennett, the 2014 fourth overall pick, found Jooris with a pass into the slot.
Jooris has been a pleasant surprise at Flames camp. Undrafted, the right-winger left Union College after three years to sign with Calgary a year ago. He spent all of last year with the American Hockey League's Abbotsford Heat.
Jooris, Bennett, Michael Ferland, Sven Baertschi and Gaudreau — who had three assists — are battling for what may end up being only one open forward job, depending on injuries.
Mark Scheifele and Cliff Thorburn scored for Winnipeg (2-4-0). The Jets and Flames (5-3-0) will wrap up the pre-season on Saturday when they meet again at the MTS Centre in Winnipeg.
Monahan, who scored 22 goals last year as a rookie, will be counted on to provide even more offence this season given the off-season departure of free agent Mike Cammalleri, the only other Flame to reach the 20-goal mark in 2013-14.
Monahan's first goal of the night opened the scoring at 8:20 into the second period. He scored his second goal off a pass from Paul Byron from 40 feet out, ripping a slapshot into the top corner.
Locked in a battle with Jonas Hiller for the Flames starting job in net, Karri Ramo had a quiet night in net. Ramo was tested only 18 times.
Thorburn's goal came on a 5-on-3 power play in the final minute of the game.
Michael Hutchinson made 21 saves for Winnipeg.
Notes: The Flames expect to have injured forwards Mikael Backlund (abdominal strain), Mason Raymond (lower body) and David Jones (lower body) back at practice on Friday... Calgary has 33 players still in camp (20 forwards, 10 defenceman, 3 goalies). The Jets still have 32 players in camp... Teams need to be down to a 23-man roster by 5 p.m. ET on Oct. 7.