With nine seconds remaining, Red Bird's Derek Davis nailed a 3-pointer to give the Cardinals a one-point lead.
Following an Evarts timeout, James Ledford put up a 10-foot shot but missed. Senior Jamie Combs grabbed the rebound, but his putback missed as he drew contact from a Red Bird player.
Evarts coach Jerry Ford, who protested the no-call, declined to comment after the game.
Brandon Roberts, a freshman guard, fired in 16 points to lead Red Bird (6-3). Davis and junior guard C.R. Berry followed with 15 and 14, respectively.
"Both teams played hard. I don't know if they played all that well, but both of them played hard," said Red Bird coach John D. Wilson.
"I thought a few calls were questionable in the first quarter, but we're just lucky enough that they missed that last shot."
The biggest lead of the night came when the Cardinals jumped out to a 5-0 advantage as Davis hit a 3 and Berry added a layup.
Ledford, who paced the Wildcats with 18 points, scored his team's first three baskets.
The game was tied at 7-7 and 9-9 before Ledford and Alex Bush each scored to give Evarts a 13-9 advantage after one quarter.
Red Bird missed 12 of its 16 field goal attempts in the opening period.
The Wildcats maintained a four-point lead early in the second quarter. Evarts was held without a field goal in the final three minutes of the period.
Paul Hoskins and Berry each had baskets and Ezra Jack hit a pair of free throws as the Cardinals tied at game at 24-24 at halftime.
Evarts was hindered by seven turnovers in the quarter.
The scored was tied three times in the third period. Red Bird had a three-minute drought but only trailed 39-38 entering the final quarter.
The teams combined to make 10 of 30 field goals in the third period.
"We're trying to get better," said Wilson.
"We're just not real good, but we're trying to do the best we can. That's what it's all about."
Red Bird outscored the Wildcats 21-19 in the fourth quarter. Davis completed a three-point play with 3:04 remaining as the Cardinals led 51-47.
Both teams had chances to pull away in the final 90 seconds, but Red Bird missed four straight free throws and the Cats missed three.
Dustin Mefford's basket with 27 seconds to play tied the game at 56. The senior forward was fouled but missed the free throw. Bush rebounded and scored two seconds later to give Evarts a two-point edge.
"Coach Ford does a good job with them. They played hard," added Wilson. "We couldn't guard Combs or Ledford or (Jarrod) Fields either. They played big."
Combs added 12 points and 14 rebounds for the Wildcats. Bush added 11 points and 12 rebounds, and Fields scored 10 points.
Evarts (1-8) must prepare for three straight district games, beginning Monday at Harlan. The Wildcats play host to Cumberland on Friday and Cawood on Jan. 9.
Red Bird returns to action Tuesday at Lynn Camp.
Brandon Roberts hit a free throw with four seconds to play as the Cardinals edged Evarts 41-40 in the junior varsity game.
Roberts powered Red Bird (2-1) with 18 points.
Jarrod Fields led Evarts (5-3) with 18 points. Bryan Tompkins scored six points. R.J. Fields, Kyle Clark and Travis Helton each added four points. Josh Combs and Trevor Smith tossed in two apiece.
Bryan Tompkins 0-5 0-0 0, Trevor Smith 0-0 0-0 0, James Ledford 8-16 0-0 18, Kyle Clark 0-0 0-0 0, Alex Bush 5-8 1-4 11, Jamie Combs 3-9 6-10 12, Jarrod Fields 4-10 0-0 10, Travis Helton 0-0 1-2 1, Dustin Mefford 2-4 2-7 6. Totals: 22-52 10-23 58.
RED BIRD (6-3)
C.R. Berry 7-13 0-3 14, Derek Davis 6-21 1-3 15, Ezra Jack 1-2 2-2 4, Paul Hoskins 3-7 0-1 6, Justin Brock 2-6 0-0 4, Brandon Roberts 5-10 3-3 16, Kyle Peters 0-0 0-0 0, Andrew Hacker 0-2 0-0 0, Donavan Nantz 0-0 0-0 0. Totals: 24-61 6-12 59.
Evarts 13 11 15 19 58
Red Bird 9 15 14 21 59
3-point goals: Evarts 4-14 (Ledford 2-5, Fields 2-7, Tompkins 0-1, Mefford 0-1), Red Bird 5-21 (Roberts 3-6, Davis 2-10, Hacker 0-1, Berry 0-4). Rebounds: Evarts 41 (Combs 14), Red Bird 25 (Hoskins 10). Assists: Evarts 8 (Smith, Combs, Mefford 2), Red Bird 8 (Berry 6). Turnovers: Evarts 17, Red Bird 12. Fouled out: None.