Skylar Diggins stole an errant pass from Kaleena Mosqueda-Lewis with 8 seconds left, and after dribbling through a few defenders, found Achonwa for the uncontested lay-in.
Kelly Faris then heaved a desperation attempt from 65 feet that fell harmlessly off the backboard, setting off a wild celebration for the Irish, who have won 26 consecutive games.
The Fighting Irish players, wearing championship hats and T-shirts, set up a dance line to celebrate and did an Irish jig in front of the school band.
Notre Dame (31-1) had been in the title game six previous times, including the past two, and lost to the Huskies in each one.
The Irish weren’t going to be denied in their final chance to win an elusive Big East championship. Earlier in the day, Notre Dame announced it would be joining the Atlantic Coast Conference starting next season.
Kayla McBride, named the tournament’s most outstanding player, scored 23 points to lead the Irish. Jewell Loyd finished with 16 and Diggins had 12.
Stefanie Dolson scored 18 points and Breanna Stewart had 16 for Connecticut (29-4), which had won the past five Big East tournament titles but fell to Notre Dame for the third time this season.
The Huskies trailed 59-53 with 2:55 left before tying it at 59. They had a chance to take the lead but Faris missed a layup. She got her own rebound and after calling a timeout, the Huskies had a chance before Mosqueda-Lewis got caught in the corner and threw the ball away to Diggins, setting up the finish.
The Irish have dominated the series recently with seven victories in the past eight meetings. No team has ever dominated the Huskies like that since Connecticut won its first national championship in 1995.
The only Connecticut victory came in the conference title game last season, but the Huskies couldn’t pull off a third consecutive win over Notre Dame in the tournament championship.
The loss ended a run of 19 consecutive seasons that Connecticut had won either the regular season or postseason conference title.
SOUTH DAKOTA STATE 56, SOUTH DAKOTA 53
In Sioux Falls, S.D., Megan Waytashek scored 11 points and grabbed a key rebound in the last minute to help South Dakota State (25-7) beat South Dakota (17-15) in the Summit League Tournament final.
Gabrielle Boever had seven steals for South Dakota State, which secured an automatic bid to the NCAA Tournament with its fifth consecutive Summit League title. She also scored nine points in the defensive struggle.
Nicole Seekamp led South Dakota (17-15) with 20 points, and Tempestt Wilson had 10 points.
The Jackrabbits shot just 29.1 percent from the field.