Sergei Bobrovsky made 26 saves for the Blue Jackets.
''We knew after the first that we needed to be much better,'' Saad said.
''Bob (Bobrovsky) kept us in it pretty much the whole first period and throughout the game. They took it to us and we knew we had to be better in the second, limit our turnovers and create chances off of their turnovers and that's what we did.''
Morgan Rielly scored for the Leafs, who can finish no higher than 29th place overall in the league.
Garret Sparks made 27 saves for Toronto.
Now solely alone in last place after Edmonton's win against Vancouver, Toronto will have either the best odds of landing the No. 1 overall pick (20 percent) or the second-best odds (13.5 percent).
The Leafs haven't had the No. 1 overall pick since 1985 when they selected Wendel Clark from the Saskatoon Blades.
The Leafs, who have two games remaining, can still finish with more points than the Oilers, though a tie would have Edmonton finish higher.
''I see where people are coming from,'' Leafs center Tyler Bozak said of lottery implications before the game. ''Obviously (fans) want the No. 1 pick and if you lose you've got a better chance of getting it so I see what people are saying. But within our room there's not one guy in here who wants to lose.''
Entering the game having lost six of nine, the Blue Jackets scored three goals in about four minutes in the third to seal the victory.
''We ended up creating a couple turnovers, got us a couple goals to go up 2-1 and I thought we made some pretty good offensive plays to score some others,'' Blue Jackets coach John Tortorella said.
Columbus got off to a slow start and didn't land its first shot until more than 12 minutes had gone by in the opening period.
Becoming the 46th player to suit up for the Leafs this season, Sam Carrick had the best chance early for Toronto, which controlled much of the first-period play. Carrick was found open in the slot by veteran Brad Boyes, but his shot attempt was stopped by Bobrovsky.
The 24-year-old was recalled from the AHL Toronto Marlies on Wednesday morning on an emergency basis, replacing Rich Clune.
The shots were 6-1 favoring the Leafs with about six minutes remaining in the first. With goals in the two previous games, including a pair in a Monday loss to Florida, Colin Greening had a terrific chance to score again late in the period. The 30-year-old had all kinds of space and time in the high slot, but his shot turned down by the Blue Jackets goaltender.
Due to be a restricted free agent this summer, Rielly opened the scoring with his career-high ninth goal this season. The 22-year-old has also posted career bests with 27 assists and 36 points. Rielly was fed short-handed by 20-year-old Frederik Gauthier, his blazing wrist shot beating Bobrovsky high blocker-side.
It was the first short-handed goal in Rielly's three-year NHL career.
''It's too bad,'' Rielly said of the losing effort in the final home game of the year. ''I think we wanted to come out and really have a good game here on home ice for the fans, but I don't think we really accomplished that.''
Saad tied it less than 10 minutes later on an error by 19-year-old Leafs rookie Kasperi Kapanen. Nearly scoring his first NHL goal half a minute earlier, Kapanen turned the puck over at the Blue Jackets blue line, springing a Columbus counter-attack.
Saad blew past the Toronto defense and sent a shot through the pads of Sparks. It was his 29th goal this season, increasing a career high.
Another Leafs turnover helped the Blue Jackets to the lead late in the second. T.J. Brennan's backhand passing attempt was picked off just outside the Toronto blue line leading to another counter for Columbus. Dubinsky finished the scoring play, roofing a shot past the glove of the Leafs goaltender.
Columbus turned the game into a blowout midway through the third. Bjorkstrand and Calvert scored less than a minute apart, joined three minutes after that by Dubinsky, who has 17 goals this season - his most in four seasons with the Blue Jackets.
Toronto coach Mike Babcock thought the mistakes would be a good primer for many of the young players in Toronto's lineup who would soon rejoin the AHL's Toronto Marlies for the Calder Cup playoffs.
''You turn pucks over, you don't play well without it, it ends up in your net,'' Babcock said. ''You turn the puck over you can't win. It's impossible. The message should be loud and clear.''
The Leafs saluted fans in attendance after the defeat, also lingering on the ice afterward to sign autographs and pose for photos.
Toronto will pick no lower than fifth at the June draft in Buffalo after selecting London Knights forward Mitch Marner with the fourth overall pick last summer.
''There's lots of good things that are going on in the organization,'' Babcock said. ''But tonight wasn't one of those things though, so let's not kid ourselves. That effort and the execution of that effort is not good enough and it's unacceptable.
''There's lots of really positive things that have gone on. I wouldn't call tonight one of them.''