The Roos, who announced new contracts for coach Brad Scott and star players Daniel Wells and Jack Ziebell in recent days, started Friday night with a 1.4.5 (38) to 0.5.6 (36) win over Melbourne at Etihad Stadium.
They ended it with a comeback 0.7.6 (48) to 0.6.8 (44) over the Tigers, after trailing until within the final minute of the game.
In between, Richmond comfortably downed the Demons 1.2.9 (30) to 0.2.3 (15), Melbourne's winless night ending a week in which they were fined $500,000 for the moves they made to secure a priority draft pick late in the 2009 season.
North fans also got to see exciting signs from the AFL's first Sudanese-born player, athletic ruckman Majak Daw, which included an impressive sidestep and running goal against the Tigers.
Richmond had controlled the early stages of their match, at one point pushing 13 points clear and despite the Kangaroos hitting back with three quick goals to take the halftime lead, Richmond again pushed clear early in the second half.
But, as was the story for the Tigers too often in last year's regular season, they gave up the lead late in the match.
With the Kangaroos within a point, Wells broke clear from a pack at half-forward and centred the ball to Aaron Black, who kicked his second goal of the match to give North the lead with 40 seconds left and Richmond couldn't regain it.
The Tigers had earlier proved far too strong for Melbourne, with a midfield led by new captain Trent Cotchin, Dustin Martin and Brett Deledio dominating.
The Kangaroos, well-served by captain Andrew Swallow in both their games, also outclassed the Demons, despite Melbourne narrowing the margin late.
The Demons had a few good signs, with Nathan Jones continuing his best-and-fairest form from last year, young midfield draftees Jack Viney and Jimmy Toumpas both looking good and big forward Jesse Hogan, who can not play in the regular season until next year, also impressing.
Melbourne coach Mark Neeld gave short shrift to the notion that the tanking investigation had had any effect on his team.
"I just want to put it on the record for the millionth time, it happened four years ago and the players and the current coaching group it didn't impact on us whatsoever," Neeld said.
"It was done and dusted at boardroom level.
"As for tonight we were pretty good, we were fairly pleased."Scott was pleased to get in the habit of winning tight games.
He said Daw was in contention to play the opening round of the season proper, although would be competing for a spot with ruck recruit Daniel Currie, who also impressed.
"He's in contention, but I think Daniel Currie was a terrific story tonight. He's one of a number of players we've got who play (Daw's) position," Scott said.
Richmond coach Damien Hardwick said it would have been nice to close out the North game, but they had an inexperienced side late in the game, with Cotchin and Deledio off, and made some mistakes.
But overall, he thought the Tigers played well without capitalising enough on the scoreboard.
"Our intensity, our ability to tackle and cause turnovers was outstanding," Hardwick said.