To do so, they need to win on the road, starting with Saturday's contest at Arizona.
Kickoff is set for 8 p.m. MDT, and the game will be televised by the Pac-12 Networks.
Now that they are on the nation's football radar after beating the Cardinal, the Utes want to remain there. The last thing they want is to earn a reputation like the team they face Saturday a decent, mid-level team that scores an upset here or there, but rarely threatens the league leaders.
The Utes want more than that.
"It was a big step for us," defensive end Nate Orchard said about the Stanford upset. "But we want a lot more wins."
Two more victories would be a milestone since it would make the Utes bowl eligible.
Hitting that mark might not seem like much of a challenge with six games remaining. However, the Utes play four of their last six games on the road. Since joining the league in 2011, the Utes are just 3-6 on the road in league play, going 2-2 in 2011 and 1-4 in 2012.
The lone win last year was the season finale a 42-35 victory at Colorado. Beating a team that won just one game last year hardly was satisfying.
"We have to make sure we get some road wins," quarterback Travis Wilson said. "That is something we lacked last year. We have to keep on pushing the tempo and motivation of this team and keep on trying to get wins."
While not ideal to have a schedule with so many road games lumped together, Whittingham believes his team will be prepared for its first road trip. More of a concern for him is that the Utes compete like they did against the Cardinal.
"Going forward, we want to accentuate the reasons for that win," he said. "We had a great week of practice, the film study, everything that went into the win is what we want to emphasize. That isn't something that this team has had a problem doing preparing but some weeks have been better than others, and last week was outstanding."
The Utes are confident they can handle the Wildcats because they match up well with them. Arizona, like Stanford, relies on its running game to get the offense going.
Running back Ka'Deem Carey, who averages 142.3 yards a game, leads an offense that is averaging 262.2 yards on the ground and 161.6 through the air.
Carey rushed for 204 yards in the Wildcats' 34-24 win over the Utes last year.
As for the Ute offense, it will be tested by a defense that is giving up just 19 points a game to rank 22nd nationally. But it has faltered in its two league losses, giving up over 34 points per contest. That vulnerability could bode well for a team that dominated Stanford for a significant chunk of the game last week.
"We are clicking on all cylinders right now, especially in the run game," running back Bubba Poole said. "We are getting good blocking and we are doing a good job."
As confident as they are, the Utes know winning at Arizona will be a difficult task.
Orchard said the team underestimated how difficult it was going to be to win on the road in the Pac-12 when the Utes first joined. They now know what to expect, and are ready to change their fortunes after two seasons of struggles, he said.
"Going to a different environment, you have to get the feel for it," he said. "But we have a lot of momentum and confidence, and that is what we need going into this game."
Utah at Arizona
O At Arizona Stadium, Tucson, Ariz.
Kickoff • Saturday, 8 p.m. MDT
TV • Pac-12 Network
Radio • 700 AM
Records • Utah (4-2, 1-2), Arizona (3-2, 0-2)
Series history • Utah leads 20-16-2
Last meeting • Arizona, 34-24 (Nov. 17, 2012)
About the Utes • Arizona is one of two Pac-12 teams the Utes have a winning record against. The other is Washington State (7-5). ... Utah co-offensive coordinator Brian Johnson got his first start and win against Arizona in 2005. ... Utah leads the Pac-12 in sacks (20).
About the Wildcats • Are on a two-game losing streak and winless in league play. ... Rank second in the Pac-12 in scoring, giving up 19 points a game but has given up an average of 34.5 points per game in its league losses to Washington and USC. ... Ranked second in the Pac-12 in rushing with 262.2 yards per game and last in passing averaging at 161.6 yards per game. ... Coached by Rich Rodriguez, who is 11-7 in his third year.