Urso, a 22-year-old rookie, collapsed in the early hours of Aug. 5 at a Columbus bar and was pronounced dead in hospital.
TFC agreed to postpone its road game in Ohio originally scheduled for Aug. 11 until Wednesday night so that Crew players could attend Urso's funeral.
But Mariner doesn't expect the passion between the geographic rivals and their supporters to be affected once the game starts.
"There's empathy from our fans and our organization but when the whistle blows we've got to get three points," Mariner said Tuesday before the Reds left for Columbus. "They'll be battling hard and so will we."
The game is part of a busy stretch for Toronto (5-14-5). The club is winless in its last four (0-3-1) after Saturday's 1-0 loss at home to Sporting Kansas City and continues to wallow at the bottom of the Major League Soccer standings, all but mathematically eliminated from playoff contention.
One bright spot for Mariner in the loss to Kansas City was the play of newly signed defender Darren O'Dea, who played his first game for the club.
The Ireland international played for his country on Wednesday in Serbia before returning to Toronto.
"It was an arduous travel for him but he got 90 minutes under his belt and that served him well on Saturday," said Mariner. "I think you'll see him get better and better. He'll probably have his legs back under him now. He was fantastic (on Saturday). He's everything I want in a central defender, and more."
After Wednesday's game, Toronto will be at Houston on Saturday before hosting Mexico's Santos Laguna on Aug. 28 in CONCACAF Champions League play.
"We've got some very difficult games," Mariner said. "We've got a difficult schedule but we'll get on with it."
Toronto beat Club Deportivo Aguila of El Salvador 5-1 to open the Champions League group stage but will face a tough test against Santos Laguna, which ousted them in the semifinal stage in the previous competition.
Only the winner of the three-team group will move on to the next round.
"We got off to a fantastic start. We're on top of the division, which is always nice," Mariner said. "The way that it's set up, you've got to try to get maximum points from your home games and then try and pick some points up away from home and if we do that then we'll probably go through.
"Santos Laguna have got players that are just back from the Olympics that won the gold medal so they're a very, very difficult team — one of the top teams in Mexico. So, it's going to be a fantastic night, a difficult night, but the boys will be ready for them."
Notes: Toronto FC announced on Tuesday that defender Doneil Henry has signed a new deal with the club. The 19-year-old from Brampton, Ont., who came up through Toronto's youth system, suffered a knee injury on Saturday. Mariner said the team is waiting for the swelling to go down before having Henry undergo an MRI to find out the extent of the damage. ... Columbus (8-8-6) sits outside of post-season contention but is still in the mix.