Kennedy, who had only allowed a home run to Carlos Gonzalez in the fourth, was rolling along.
But Norris, normally the team's starting catcher who got his seventh start of the season at first base on Sunday, dropped Nolan Arenado's popup near the bag to extend the inning.
At that point, Kennedy figured he could still get out of the inning without issue.
"Right then, I said, 'I got you,'" Kennedy told Norris. "Two pitches later, it was a different ballgame. My whole goal was to pick him up. You're still trying to win that ballgame and not let it get out of hand."
Ben Paulsen doubled and the Padres intentionally walked DJ LeMahieu to get to McKenry, who knocked in three runs with a double to the gap in right-center.
"It's really unfortunate. Derek's played an awful lot of games for him, he's given us everything he's had, I'm sure he feels horrible about it," said Padres interim manager Pat Murphy.
"We've all had that happen to us. It's just unfortunate when it happens in the [seventh] with two outs in a close ballgame and the opposing team takes advantage of it so much. Derek plays very, very hard, and I'm sure he feels awful about it."
This was a rare time Sunday when the Padres' defense let down Kennedy, who allowed four runs, but only one earned, in 6 2/3 innings with eight strikeouts.
In the third inning, third baseman Cory Spangenberg fielded a McKenry's ground ball down the third-base line. With his momentum carrying him into foul territory he made a strong throw to get McKenry, with a nice dig out of the dirt by Norris.
One play later, second baseman Jedd Gyorko made a diving stab of a line drive by Matt McBride.
"Fastball location was good, curveball was good today," Kennedy said. "I was getting ahead of guys and my defense made some good plays behind me."
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.