New Zealand, meanwhile, can secure their progression to the knockout stages with a victory after beating South Korea in their opening game.
Competing in only their third Olympics in football, New Zealand are aiming to progress from the group stage for the first time in their history.
West Ham United defender Winston Reid, who is captaining this team as one of their three over-age players, made a superb goal-line clearance in the second half to keep the scoreline level against South Korea, who dominated the majority of the match.
Moments later, though, Burnley striker Chris Wood struck from around the penalty spot to provide New Zealand with a valuable lead against the run of play in the 70th minute, with their Asian opponents unable to find an equaliser.
As such, another win against Honduras on Sunday will see Danny Hay's side go a step further than ever before in this competition with a game to spare.
Honduras, meanwhile, have a proud record at the Olympics in football, having qualified for four of the previous five men's tournaments.
They reached the quarter-finals in London in 2012 before finishing fourth at the last Olympics in Brazil, so Thursday's 1-0 defeat at the hands of Romania would have hit the nation very hard indeed.
Perhaps what made the loss all the more painful was the manner in which it came about, with Andrei Ciobanu's inswinging corner causing havoc in first-half injury time.
At first, it looked like Romania's number ten's corner had gone all the way in, but on second viewing it became clear that Elvin Oliva's glancing header had diverted the ball past his own goalkeeper.
Miguel Falero's side must avoid defeat against New Zealand on Sunday, otherwise they will crash out of the group stage for the first time since 2008 in Beijing.
New Zealand are unlikely to disrupt a winning formula for Sunday's game.
Much of their hopes will hinge on the experience and quality of Reid and Wood once again, with the pair boasting 83 senior caps between them.
Honduras, however, could make a few changes as they look to improve their performance and result.
Brayan Moya, who is one of two over-age players in the squad, is likely to start in midfield having been an unused substitute on Thursday.
Oliva could be taken out of the firing line, too, having been booked before scoring his own goal in a disappointing individual performance against Romania.
New Zealand Under-23s possible starting lineup:
Woud; Ingham, Pijnaker, Reid, Cacace; Stensness, Bell, Lewis, Just; McCowatt, Wood
Honduras Under-23s possible starting lineup:
Guity; Melendez, Maldonado, Garcia, Decas; Rivas, Alvarez, Moya, Rodriguez; Martinez, Benguche
We say: New Zealand Under-23s 0-0 Honduras Under-23s
We are struggling to see many clear-cut chances being created in this match, with both sides adopting safety-first approaches.
The pressure is on Honduras to take the game to their opponents, but we can see New Zealand remaining resolute and gaining a positive result to take a step closer to progression.
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