Some Bulls fans, with good reason, might start to feel nervous about a two-game win streak. After all, the whole point of rebuilding is to collect a few high draft picks, especially next summer.

The Bulls had a chance to make it two victories in a row, leading New Orleans by 7 points at the start of the fourth quarter on Saturday at the United Center.

But maybe there's no need to worry. The Bulls' lack of go-to scorers late in games figures to be a recurring problem. They went scoreless over the final 2:29 of the fourth quarter and lost 96-90 in overtime.

The Bulls (2-6) set a franchise record with 42 attempts from 3-point range, but they made just 11 of them for 26.2 percent.

"I'm proud of our guys going out there and competing when the ball wasn't going in the hoop, and giving ourselves a chance," Bulls coach Fred Hoiberg said. "They continue to go out there and battle and do everything we're asking of them."

The closest the Bulls came to a game-winning bucket was when Robin Lopez had a running bank and putback attempt roll off the rim with 9.7 seconds remaining in regulation. Lopez (14 points, 9 rebounds) has virtually no experience in the NBA as a late-game scorer and he didn't feel good about the close calls.

"I think we played so well, especially coming back in the game and tying it up," Lopez said. "I felt everybody else was great. I honestly feel that's a game where I look back right now and I feel like I missed some big shots. I didn't make a couple plays that I should have.

"I feel otherwise my teammate played such a fantastic game. I'm going to be better next time."

The Bulls led by 9 points on several occasions in the second half. They coughed up the lead with a flurry of turnovers and New Orleans went ahead 77-71 with 5:47 remaining.

Long-range shooting helped -- to a point. Lauri Markkanen and Denzel Valentine each hit a pair of 3-pointers to put the Bulls ahead 83-81 with 2:29 left, but couldn't score for the rest of the fourth quarter.

New Orleans (5-5) scored the first 4 points in overtime. Jerian Grant got some of it back with a 3-point play. The Pelicans then connected on a Anthony Davis alley-oop and Lopez was called for a 3-shot foul on DeMarcus Cousins. The burly center hit 2 of 3 at the line to boost the lead to 91-86.

Trailing by 5 points with just over a minute left, the Bulls got three looks from 3-point land on the same possession, but none of them dropped. A 3-pointer by New Orleans veteran Jameer Nelson made the score 96-88 with 48.9 seconds left, essentially icing the game.

Hoiberg was asked how he approaches late-game situations with no reliable scoring star to run an isolation.

"It's a good question," he said. "A lot of it is just based on how the game is going."

Justin Holiday led the Bulls with 18 points. Valentine scored 16 and was the Bulls' best 3-point shooter, going 4-for-7. Guard David Nwaba left the game after turning his right ankle in the third quarter and did not return.

For New Orleans, Chicago native Davis piled up 27 points and 16 rebounds, while Cousins had 25 and 11.

Markkanen (2-for-11) and Holiday (3-for-10) were off-target from 3-point range, but Hoiberg didn't second-guess the 42 attempts.

"They're so long in the paint, we had an emphasis of driving into the paint, trying to get a touch there and kick out, spray out for shots," Hoiberg said. "A lot of those were good, uncontested looks. We're going to shoot those."

Twitter: @McGrawDHBulls