Looks like Smytty ends up...

#4 All Time
Smytty's three goals in 2:01 did beat a Wayne Gretzky record (oh no, Wayne's getting erased from the Oiler record books....) but now the name Bill Mosienko has been bounced around once again since the Smytty feat.
Mosienko scored three goals in 21 seconds in 1952 for Chicago in the last game of the season. Both the Rangers and the Black Hawks were already out of the playoffs in a meaningless game that only saw just over 2000 fans. Rumour has it that a young Stan Fischler (the model for the shortlived sailor logo the Isles had a few years ago?) was a cub reporter at that game.
The Rangers goalie Lorne Anderson had already been shelled for 10 goals in his two previous game for the team and never played again after that in the NHL.

2nd fastest...
Jean Beliveau 44 seconds

3rd fastest...
Carl Liscombe of Detroit 1:04 1938

4th fastest...
our own mullet man also just edged out...

5th fastest..
Peter Bondra scored three goals in 2:06 while a Capital

6th fastest....
Wayne Gretzky scored three goals in 2:18 vs. St. Louis in a 9-2 rout in 1981. Gretzky also scored four goals in 7:58 in that game and five goals total.

7th....
Don Maloney of the Rangers scored three in 2:30 vs. Washington in 1981

If anyone has any more research to add to this, please do. It was tough enough finding these stats. There may be other records I've missed. I noticed no one out there had yet determined where Smytty stood overall in NHL history with his trio of quick garbage goals. Hopefully no more records pop up and Ryan Smyth remains with the fourth fastest three goals in NHL history.