After falling to St Kilda on the Gold Coast in round 13, the Kangaroos have responded with gritty wins over Port Adelaide and Collingwood.
The victory over the Pies pulled North back into the top eight, after it faced the challenge of shrugging inconsistency to secure a finals berth.
Grant recognises that challenge is still alive and nothing changes for Sunday's encounter with bottom-placed Melbourne.
"It's pretty hard to come out and say, 'You've got to beat the teams you're expected to beat'," he said from Arden Street on Tuesday.
"It's a pretty even competition and, if you're five or 10 per cent off, any side's capable of jumping up and hitting you between the eyes and beating you.
"I don't think it's a matter of beating the sides that we're expected to beat. It's just a matter of being consistent and performing at a consistent level every week."
Grant added that the efforts of the last fortnight have had a significant impact on his teammates.
"Our interstate trips have been well-documented that they haven't been great, but especially with the last two wins we've really started to build some momentum," he said.
"There's a really strong belief amongst the group at the moment and we've just got to continue to be consistent in all areas that we focus on.
"If we do that, I think we'll certainly give a few teams a shake in the run to September."
Asked whether he felt North Melbourne's current side is better than its 2007 outfit, which won its way to a preliminary final, Grant was optimistic.
"I think we are," he said. "I think over the last two or three weeks, that consistency that we've been able to build on, it probably puts us in a good position to really give it a decent tilt this year.
"The players are really starting to contribute and they can perform on the bigger stage.
"We got whacked between the eyes a few times last year, but that was last year and I think so far this year we've shown that we can match it with the better sides in the competition."
The Kangaroos' run to the finals includes rematches with top two sides Geelong and the Western Bulldogs.
They lost to the Cats by 13 points in round 11 and beat the Bulldogs by three points in a round-nine thriller.
