Napier scored 26 points and Giffey added a career high 16 points in their final home game to lead 19th-ranked UConn (24-6, 12-5 American Athletic Conference) to a 69-63 win over Rutgers on Wednesday night.
Napier made a career-high seven 3-pointers and hit eight of his 13 shots from the floor. Giffey was 4 of 7 from behind the arc.
''We're the captains on this team, so who else is going step up?'' said Giffey. ''As a senior, you've got to work with those emotions. We were so pumped up and hyped up for this game, it was just easier to play for us, I guess.''
Myles Mack scored 16 points for Rutgers (11-19, 5-12), which hasn't beaten the Huskies in Storrs since 1972. Wally Judge added 13 points and 10 rebounds.
Connecticut led by three points at halftime and by 11 points in the second half after an 8-0 run. Two dunks by Philip Nolan made it 64-53 UConn and forced Rutgers coach Eddie Jordan to call a timeout.
But the Scarlet Knights began chipping away at the lead, and cut the lead to 67-63 when Kadeem Jack stepped in front of a DeAndre Daniels pass and made a dunk at the other end with a minute left in the game.
Daniels redeemed himself seconds later when he blocked a layup attempt by Judge and hit a free throw on the other end. Nolan then drew a charge on the baseline, and Napier sealed the game from the foul line as the fans chanted ''M-V-P.''
The Huskies won despite scoring just three points in the final four minutes, after failing to get a field goal in the final 7 1/2 minutes in a win over Cincinnati on Saturday.
''Offensively, we've got to figure it out when it comes down the stretch,'' Napier said. ''But I cannot stress enough that defense is going to help us win games.''
UConn shot 47 percent from the field, while Rutgers hit on 44 percent, after making just one of their first nine shots, as the Huskies jumped out to an early 10-3 lead. Rutgers got hot after that, scoring the next eight points to take the lead.
The crowd got into the game after Amida Brimah, the Huskies 7-foot freshman, blocked a shot into the first row, and another off the backboard, forcing a shot-clock violation on Rutgers. That sparked an 8-2 run that gave UConn a 27-20 advantage.
The teams started trading 3-pointers, hitting 14 of them before intermission. Mack hit all three of his shots from behind the arc for Rutgers.
Napier made 4 of 6 and Giffey was 3 of 6, helping UConn to a 34-31 lead at halftime.
''We wanted to have a 3-point contest,'' Napier joked.
UConn finished 12 of 25 from behind the arc. Rutgers was 8 of 18.
It was an emotional senior night for Napier, Giffey and center Tyler Olander. They won a national title as freshmen, then stuck with the program through the retirement of Hall of Fame coach Jim Calhoun and academic sanctions that kept them out of last year's NCAA tournament.
''They kept this program alive,'' said coach Kevin Ollie. ''I owe them a lot.''
It was the final scheduled meeting between the two longtime conference rivals. Rutgers heads to the Big Ten next season. UConn improves to 37-14 in the series, and has won 21 of last 23, including an 82-71 win in New Jersey in January.
Rutgers has lost five of their last six.
''Their defense picked up and we just had to execute better,'' said Rutgers coach Eddie Jordan. ''We didn't convert a 1-on-1 fast break at the rim, and that's a big play.''
Connecticut came into the night with a remote shot at a share of the American Conference championship, but Louisville ended that hope with a win over SMU. The Huskies are now tied with SMU for third place in the league, but the Mustangs hold the tiebreaker, having beaten the Huskies twice.
UConn closes the season Saturday at Louisville. SMU plays at Memphis.
Rutgers, the seventh seed in the conference tournament, hosts Cincinnati on Saturday. The Scarlet Knights which beat Central Florida by two points on Saturday, have not won back-to-back games since beating Army in December and Temple on New Year's Day.
Napier needs just two points to catch Kemba Walker and move into seventh place on the school's all-time scoring list. His four assists Wednesday put just nine behind Ollie for third place on that list.