"I told my wife at breakfast I think Brandon is going to have a great game tonight," the New York Knicks coach recalled. "He said some things at the shootaround about taking a shot.
"I knew he was going to be good. He gave us a couple of big baskets when we really needed it."
Derrick Rose and Carmelo Anthony scored 20 points apiece to help the Knicks (11-9) go two games over .500 for the first time since Nov. 21, 2015. For only the third time in 15 years, the Knicks are over .500 after the first 20 games.
Rose hit the 20-point mark for the third time in his past four games.
Kristaps Porzingis contributed 15 points, 14 rebounds and four blocked shots for the Knicks, who are 9-3 at the Garden.
Sacramento (7-13) lost its third straight, all on the road. The Kings trailed by as many as 21 points in the second quarter before fighting to get within one point with a strong third quarter.
DeMarcus Cousins paced the Kings with 36 points, 12 rebounds and three blocked shots. It marked the 10th time Cousins has poured in at least 30 points this season. He was 14 of 16 from the foul line but 9 of 30 from the floor.
He also picked up his league-leading seventh technical foul.
Rudy Gay added 22 points and nine rebounds for Sacramento.
Anthony scored five of the Knicks' final seven points to preserve the win.
Willie Cauley-Stein's three-point play closed the Knicks' lead to 96-94 at the 4:51 mark, but Anthony's 3-pointer pushed the margin to 99-94 with 3:24 left.
A layup from Jennings gave the Knicks a 92-85 edge with 6:48 to play. He scored eight points in the quarter and was 4 of 4 from the line.
"Our defense picked up in the fourth quarter," Jennings said. "We just trusted in the process, trusted each other."
New York was outscored 36-26 in the third quarter but held onto an 81-77 lead.
A 20-2 burst got Sacramento within 74-73 with 1:24 remaining in the third.
The Knicks shot a sterling 47 percent (8 of 17) from beyond the 3-point arc in the first half and led 55-41 at the break. The Kings committed nine turnovers in the half and shot just 28.6 percent from the floor.
A 3-pointer from Garrett Temple got the Kings within 48-38 with 2:45 left in the second.
New York opened the second quarter with a 22-4 run, extending its lead to 48-25. Jennings fueled the onslaught with two of New York's four 3-pointers.
"We can't keep falling behind like this and expect to keep digging out of a hole," Kings coach Dave Joerger said. "We had that nice run in the third, but we made too many mistakes, bad passes to overcome."
Rose produced a stellar first quarter, scoring 10 points and dishing out three assists to help the Knicks to a 26-21 lead. Cousins poured in 14 points.
Overall, New York outshot Sacramento from the floor 44.3 percent to 32.3 percent. The Kings had a big edge at the foul line, making 27 of 31 to the Knicks' 17 of 24, while New York compiled a 58-50 rebounding advantage.
NOTES: Kings C DeMarcus Cousins was a surprise visitor at the NBA store in New York City on Saturday, helping a Sacramento family and five underprivileged children in New York pick out items. ... The Knicks were without G Courtney Lee (sprained ankle). ... Cousins and Knicks F Carmelo Anthony were teammates on the United States' gold-medal-winning team at the Rio Olympics. ... Knicks C Joakim Noah started after missing the previous two games with a sprained ankle. He finished with two points and five rebounds in 25 minutes and was 0 of 4 from the foul line. ... Kings F Arron Afflalo averaged 12.8 points per game last season with the Knicks. ... The Knicks play Tuesday at Miami. ... The Kings head to Dallas to face the Mavericks on Wednesday.