Francis added six of his season-high 26 points in the overtime. Marbury and Francis scored all of New York's 17 points in the extra period and 33 of the Knicks' last 35 points.
"It was exciting because we were down. We never felt like we were going to lose," said Marbury, who played 51 of 53 minutes.
Marbury hit on a three-point play to give the Knicks the lead for good in OT at 93-90 with 3:44 left and added a 3-pointer 37 seconds later for a 96-90 lead.
Marbury was 6-of-14 from behind the arc, but said, "I don't consider myself a 3-point shooter."
He was shooting at 42 percent before Saturday night, connecting on 300 of 714.
Marbury, who had 34 points Friday night in a 106-97 win over Golden State, also had nine assists. It was the second consecutive win for the Knicks after going 10 straight games of winning one and losing one.
New York pulled within a game of New Jersey for eighth place in the Eastern Conference.
Francis played 41 minutes off the bench after starting guard Quentin Richardson only played the first 10 minutes before leaving with a sore lower back, an ailment that cost him 11 games earlier this season.
"I haven't played 41 minutes in two years," said Francis, a three-time All-Star who was traded by Orlando in February 2006 and averaged a career-low 14.4 points.
This season he has been hampered by right knee and ankle problems, missing 33 games and averaging 9.1 points. He decided to play again after New York lost starting guard Jamal Crawford to ankle surgery earlier this week.
"I guess it's belief. I'm not hiding anything from anybody. I'm still injured. I'm not 100 percent but I'm going to give it what I've got," Francis said.
Marbury made 10 of 11 free throws, including 5-for-5 in the fourth quarter and overtime. Francis was 8-of-13 overall and 6-of-11 in the final period and OT.
"Marbury's been on a roll, and once Francis got going it was tough to stop them," said Atlanta coach Mike Woodson. "They were penetrating and getting to the free-throw line. We were settling, and we didn't get to the line. I thought that was the difference coming down the stretch run."
The Hawks, who have lost seven of eight, got within 103-100 on a 3-point basket by Joe Johnson with 51.5 seconds left. Johnson led the Hawks with 32 points.
"We couldn't come up with the big plays down the stretch," Johnson said. "It's frustrating, but it's been a trend of ours all year."
The Hawks blew a 67-52 lead late in the third quarter, but managed to go to overtime when Johnson made an easy dunk with 50 seconds left to tie it at 87 after Tyronn Lue stole an inbounds pass.
The Knicks took an 87-83 lead with 3:08 left in regulation on a pair of free throws by Francis, who scored 10 points in the quarter. But Josh Smith, who finished with 20 points and 11 rebounds, made a pair of free throws with 2:03 left to get Atlanta within 87-85 before Johnson tied it.
Marbury had a chance to win it in regulation, but his driving layup slid off the rim at the buzzer.
Smith also had three blocks, making him the youngest player in NBA history with 500 career blocked shots (21 years, 88 days). Smith is in his third season, a first round draft pick after playing his senior season at Oak Hill Academy in Virginia.
"It feels good. It's another stepping stone," he said. "It's bittersweet, because we lost. It would have been great to get the record and a win."
The Hawks led 49-37 at the half with Johnson scoring 17 points, including a 3-pointer at the halftime buzzer. Johnson scored 12 straight points in the opening quarter to give Atlanta a 23-13 lead, which the Hawks stretched to 31-15 at the end of the period on 3s by Anthony Johnson and Josh Childress.
The only other New York player in double figures was Renaldo Balkman, who had 12 points and 13 rebounds.
Marbury had 11 points at halftime and Francis, who came off the bench, had only three.
- Hawks center Lorenzen Wright sustained what was originally diagnosed as a facial contusion during the first quarter of Friday night's 93-92 loss at Washington. Further tests on Saturday showed that Wright had suffered a concussion. He sat out the game.
- The Knicks were without G Nate Robinson, who missed his third straight game due to a stomach virus. Also out was F David Lee, who missed his fifth straight with injuries to his leg and ankle.