The Lady Hounds overcame sluggish starts in both the first and third periods to set up the thrilling finish.
Trailing 52-42 with 4:30 minutes remaining, Newport closed the game on a 15-6 run and had three shots for the win in the final :15 seconds only to lose the offensive rebound out of bounds with :1.5 to go.
Rivercrest jumped out to a 20-13 lead at the end of the first quarter with Lady Greyhound guards D'Jharion Lee and Taelehs Williams both sitting on the bench with two fouls each after the game's first eight minutes.
Newport outscored the Lady Colts 19-7 in the second period to take a 32-27 lead into intermission, before stumbling again in the third.
Rivercrest grabbed a 46-41 advantage heading into the final frame and widened their lead to 10, 52-42, at the halfway mark of the fourth before the furious Lady Hound rally.
Tyrena Friar and Tamela Steward led Newport with 16 points each while Lee added 9. Dashyrah Ellis had 7 points followed by Williams with 5 and Khnedee Finch with 4.
The Lady Greyhound win came a little more than 12 hours after Newport defeated Pine Bluff Dollarway on the road Friday night to open 2-4A conference play.
Newport took a 14-4 lead in the first quarter and never trailed despite "playing less than our best," according to Coach Amee McGuire.
Newport led 33-11 at halftime and 43-17 at the end of the third quarter.
Friar led Newport with 25 points, Lee add 10, Williams had 8 points while Ellis chipped in with 7. Ellis had 7 points, Steward 4 and Finch 1 to round out the scoring.
In other tournament action Saturday:
Nettleton knocked off Bay 59-54 to capture the boys championship and Cedar Ridge upended Sylvan Hills 46-35 in the girls championship contest.
Brookland's boys defeated Cedar Ridge 59-45 for third place on the boys side while Rivercrest knocked off the Batesville Pioneers 63-52.