Roman, 13-2 overall and 7-0 in Catholic League action, beat the Saints (10-4, 5-1) for the first time since 2007.
"It's a nice win," said McNesby, whose team made 11 of 13 free throws in the fourth quarter. "We have a lot of respect for Neumann. But our goal is to win the league championship. We have to work hard every day."
Carr's senior backcourt mates also produced, as Rashann London (ticketed for Drexel) and Penn State-bound Shep Garner scored 17 and 14 points, respectively. TreVaughn Wilkerson, a 6-foot-6 junior forward, had six of his eight points in the last five minutes.
The 6-foot-2, 180-pound Carr, who joined the Cahillites after playing last season for Abington Friends, shot 6 for 9 from the field and 2 for 2 from the line and sank his only three-point attempt.
"He's doing a great job of running our team," McNesby said. "He sees the floor well, plays with a lot of poise, and he's picking it up on the defensive end."
Carr might have inherited the calmness from his father, Anthony, who was a standout floor general at Parkway, of the Public League, and Cheyney.
"He had a mentality going into games that no one could stop him," Tony Carr said. "I try to play the same way."
Wilkerson's inside bucket gave Roman a 61-58 edge with 1 minute, 25 seconds to play. That's when the Saints opted to commit intentional fouls and test the Cahillites' acumen from the line. They responded by making 10 foul shots in a row.
"Coach McNesby always says, 'Making free throws and playing good defense are going to win us games,' " said Carr, whose two makes with 14.1 seconds to go made it 69-64.
Ja'Quan Newton, N-G's usual catalyst, was held to 11 points. The senior guard and Miami recruit, who collected nine boards and six assists, was just 4 for 20 (2 for 8 on treys) from the field.
"It wasn't one guy," McNesby said of keeping Newton in check. "It was absolutely a team effort."
Neumann-Goretti 18 10 15 21 – 64
Roman Catholic 12 16 16 27 – 71
NG: Lamarr Kimble 26, Troy Harper 14, Tony Toplyn 7, Ja'Quan Newton 11, Quade Green 3, Vaughn Covington 3.
RC: Tony Carr 15, Rashann London 17, TreVaughn Wilkerson 8, Manny Taylor 6, Shep Garner 14, Gemil Holbrook 8, D'Andre Vilmar 3.
Roman Catholic coach Chris McNesby talks about the big win. www.inquirer.com/rallypa