As Tom Paris and Harry Kim are taking the Delta Flyer for a test run, another small alien ship pulls alongside them. The alien pilot, Irina, challenges them to a race. As the two ships race through an asteroid field, Irina's ship begins filling up with nyocene gas. They beam Irina to their shuttle and bring her and her ship back to the U.S.S. Voyager. While making repairs, she explains to them that she is entering a race in a couple of days. This prompts Paris and Kim to convince Captain Janeway to let them enter the race too.
Meanwhile, B'Elanna Torres has been frantically trading favors with crewmates so she can borrow enough holodeck time for her and Paris, her boyfriend, to have an entire weekend to themselves. When Paris explains to her that he forgot about the getaway weekend and entered the race, she tells him that she does not mind. Later, she confesses to Neelix that she was very hurt that Paris forgot about something that took her so much time to set up. She tells Neelix that she thinks things might be ending between Paris and her.
When Janeway registers the Delta Flyer in the race, she learns from O'Zaal, the race coordinator, that the race is the first step towards peace for the four different cultures living in the area. Each of the different species has been at war to control the area for nearly a century. This race marks the first time the four of them have ever competed peacefully.
Seven of Nine tells Torres that she has embraced some of Paris' interests and it has made him easier to work with. Taking Seven's comment as good advice, Torres convinces Kim to let her fly with Paris as co-pilot of the Delta Flyer. Paris is bewildered when Torres shows up in Kim's place wearing a flight suit, but he welcomes her as long as she remembers that they're there to win. The two ride in fourth place for much of the race, but they eventually manage to take the lead. Just as they get into first place, O'Zaal calls a temporary stop, saying that one of the racers has had an accident.
Irina's control panel had malfunctioned and electrocuted her co-pilot, which was later determined to be intentional sabotage. O'Zaal decides to continue the race the next day. Kim offers to help Irina fix her ship and also fly as her new co-pilot, which she is hesitant about, but lets him do. Paris and Torres notice that Kim and Irina seem to be forming a relationship, which causes Torres to wonder how good of a match she and Paris are.
When the race continues the next day, Torres is distracted by her thoughts and Paris can sense something is wrong, but the Delta Flyer manages to maintain its lead. Irina and Kim have successfully fixed Irina's ship and begin to catch up with the others almost immediately, keeping track of the Delta Flyer the whole time on their computer.
When Paris finally asks Torres what is bothering her, they get into a heated discussion. Paris is determined to work things out, but Torres sounds like she is ready to give up. Paris stops the Delta Flyer and tells her they are not going to move again until they work it out.
Meanwhile on Irina's ship, her control panel malfunctions again, almost electrocuting Kim. Kim suspects that Irina sabotaged her own ship and has his suspicions confirmed when she points a phaser at him. He manages to wrestle the phaser away from her and finds she has disabled the com system, so he just stops the ship and holds her at gunpoint. When Irina seems strangely interested in the Delta Flyer's progress, Kims realizes that she has sabotaged that ship as well. She admits to him that the fuel converter on the Delta Flyer is rigged to explode at about the time it crosses the finish line, killing all of the spectators and officials in the area.
As Paris and Torres are beginning to work out their problems, Kim sends them a message about the fuel converter. They check their computer and discover that it will explode in a matter of minutes. They pilot the Delta Flyer to a nearby nebula and eject the warp core. The nebula contains the explosion and the Delta Flyer gets safely away.
After the race is over, Paris and Torres take the Delta Flyer out again on a more personal mission — the back of the ship now reads "Just Married."