The Crew, who have home advantage this weekend, have won 10 and drawn two of their last 15 matches, while the visitors can boast nine victories in 11 games going into this clash.
Columbus had the edge in the regular season, recording a 2-1 away win at the end of July and a 1-0 home victory in September, but New England did have the last word when prevailing 2-1 in early October.
"It's going to be a tough battle, playing them home and away, but between us and them, we have been kind of neck and neck, so it is going to be an interesting and exciting match-up," said Columbus forward Justin Meram on the club website.
Defender Tyson Wahl added: "We've had a fun series in the regular season, we've created what feels to me like a mini rivalry.
"We've had some great games, some competitive games. It's a team that we respect and we know they are good, but we are also confident that we can beat them and we aren't scared to play against them."
New York Red Bulls host conference table toppers DC United first in the other Eastern semi after the former beat defending MLS Cup champions Kansas City in the knockout round of the play-offs.
France legend Thierry Henry returned to action after an Achilles problem as the Red Bulls came from behind to win 2-1 on Thursday, with former Manchester City star Bradley Wright-Phillips scoring both goals.
Seattle Sounders enjoyed the best regular-season record in the Western Conference and will travel to Dallas for the first leg of their semi.
Real Salt Lake entertain LA Galaxy in the other tie in this section, with Robbie Keane expected to shrug off a hamstring injury and play alongside Landon Donovan for the visitors.
"They have some incredible players and they’re a really good team," said Real captain Kyle Beckerman. "It’ll take everything we’ve got to get past them."