Viktor Stalberg also scored in regulation for Toronto (4-1-0).
Pittsburgh was 68 seconds away from winning the game in regulation, before Kadri snuck in off the wing and buried a rebound over Penguins goalie John Curry to tie it 2-2. It was the longshot rookie's second goal of the preseason.
"Hopefully, I'm making the decision hard," Kadri said. "I appreciate (coach) Ron (Wilson) giving me the opportunity to go out there in some big situations. I think it's really building my confidence."
However, Pittsburgh came out with plenty of energy and got an early jump on the Maple Leafs. The Penguins worked the puck around Toronto's end for a full shift before Bayda lifted a backhander over Vesa Toskala 1:43 into the game.
"We had a puck stop on the goal-line tonight and we had a couple of other good chances," Penguins coach Dan Bylsma said. "That's what you want to see in the preseason, you want to be generating chances and seeing how the team plays in its own zone."
It was a big goal for Boyda, the 28-year-old from Saskatoon, Saskatchewan, who is attending training camp on a tryout after spending eight years in the Carolina Hurricanes organization.
Conner, another bubble player fighting for a spot with the Penguins extended the lead to 2-0 with his second goal of the preseason. The former Dallas Stars winger found himself with a long breakaway when Leafs defenseman Mike Komisarek pinched in from the point and Conner beat Toskala with a nice backhand deke at 12:48.
The Maple Leafs line of Stalberg, Tyler Bozak and Christian Hanson combined to narrow the score to 2-1. Hanson worked the puck in front of the goal and Stalberg ended up slamming a rebound behind Brent Johnson at 7:33 of the second period.
The trio of rookies have all shown potential in the pre-season, but there might not end up being room for any of them on the roster. The Maple Leafs are still carrying 36 players and will need to get down to 23 before hosting Montreal in the season-opener on Oct. 1.
"Have they stolen anybody's job? Not in my estimation," Wilson said. "A lot of guys are going to have to start in the minors (and) bide their time."
Newly acquired Leafs winger Phil Kessel watched from the press box ... Toronto was 3-1-0 against the Penguins last season ... The Maple Leafs assigned forwards Andre Deveaux, Ben Ondrus, Alex Foster and Ryan Hamilton to the AHL's Toronto Marlies before the game ... The announced attendance was 18,910 -- roughly 7,000 more than the Toronto Blue Jays drew down the street at Rogers Centre.