Anor had not scored since getting his first two goals of the season vs. Philadelphia on March 22 but struck with laser precision from distance in the 56th and 75th minutes.
Montreal (3-10-5) lost its third straight and Impact coach Frank Klopas said it literally was a case of his players not stepping up. Both Anor goals came from outside the penalty after he found time and space.
"I think we could have stepped on him a little bit quicker and we didn't," Klopas said.
Columbus goalkeeper Steve Clark made five saves and was spectacular in shutting down the Impact after Di Vaio's goal in the 35th minute.
Clark kept the match level at 1-1 in the 62nd minute with a diving stop of Felipe Martins then followed two minutes later with rapid-fire denials of Di Vaio and a second-chance effort from Andres Romero that brought the sellout crowd of 21,112 in Crew Stadium to their feet.
Moments after Columbus (5-8-7) forward Aaron Schoenfeld sent a glancing header off the right post, Clark lunged left to his left for another save on Romero in the 69th minute.
"(Anor) scored two fantastic goals but Steve was our man of the match," Columbus coach Gregg Berhalter said.
The Impact felt the Crew were ripe for the taking because Columbus was 0-3-4 in its previous seven matches and coming off a loss to Sporting Kansas City on Wednesday while Montreal was idle.
"It's games like this you feel you've got to get something out of it," Klopas said.
Instead, the Impact fell to 0-6-3 on the road with another away match Thursday at Real Salt Lake.
"We've got to get results," said Montreal captain Patrice Bernier. "There's a short, short window left for us to believe that something can be done. After that, you start thinking maybe next year."
Klopas gave Ohio native Evan Bush his first MLS start of the season and third of his MLS career over Troy Perkins.
"There are moments in the season when one guy's not in the best form and the other guy is," Klopas said. "You have to reward the guy who is."
Montreal started well in front of Bush as Di Vaio continued his hot stretch with his fourth goal of the season and third in the past four games.
The Impact took advantage of a turnover by defender Michael Parkhurst, who prior to the match was named to the MLS All-Star team that will face Bayern Munich on Aug. 6 in Portland, Ore.
Justin Mapp plucked the ball from his feet and fed Di Vaio on the right wing. Di Vaio did the rest from there, faking Costa Rican World Cup defender Giancarlo Gonzalez then driving the ball past Clark from just inside the box.
It was the sixth time in 10 home games that the Crew conceded the first goal.
Montreal's Jack McInerney missed an open look that would have made it 2-0 in the 54th minute and Anor made the Impact pay with his strike from the top of the arc two minutes later and a screaming blast from 25 yards for the victory.
"That's the first time this season that I can say I'm at a loss of words," Montreal defender Heath Pearce said. "Of course it feels like since the very first game of the season we've been swimming against the current."