"We're just a young team and we play extremely hard," Bledsoe said. "Even though things weren't going our way, we fought through."
Bledsoe hit a long 3-pointer with one second left on the shot clock to give the Suns a 95-85 lead with 1:25 to go.
"I just locked in a little bit," Bledsoe said. "I saw time was running down and I wasn't shooting well from 3, but I locked in a shot it with confidence."
Morris similarly has upped his game. He shot 9 of 12, and has gone 30 for 38 from the field over his past three games while averaging 24.7 points in that span and playing solid defense.
"The first two years I couldn't play without fouling," Morris said. "I watched a lot of film and became a student of the game. I saw why I was picking up dumb fouls. It's a matter of doing the work early."
Morris is only the third player since 1989 to notch three consecutive games shooting at least 75 percent from the floor while taking at least 12 shots, joining Dwight Howard and Charles Barkley.
Suns coach Jeff Hornacek became the first coach in franchise history to win his first four home games.
Anthony Davis, who entered the game averaging 23 points and 11.5 rebounds per game, was held to 14 and 12.
"Most of the game it was easy for other guys on their team to get shots so they didn't need to feed him too often," Hornacek said.
Morrow's long jump shot with 6:30 remaining pulled New Orleans within 80-79, but he missed a 3-pointer that could have given the Pelicans their first lead since the final 90 seconds of the first half.
After Brian Roberts missed a second-chance jumper following an offensive rebound by Davis, the Suns sprinted downcourt and Morris hit a 3-pointer from the left wing. Morris added a dunk and Phoenix went on a 9-2 run to open an 89-81 lead with 3:31 to go.
"We've got to continue to stay with it," Morrow said. "These grind it out games are good for us where we're the youngest team in the NBA. I think we are just ticking up. We have to keep it going."
Eric Gordon's 3-pointer made it a five-point game, but Dragic and Bledsoe hit 3-pointers to extend the Suns' lead to ten.
The Suns, who missed their first 10 3-point attempts and made only one 3-pointer through the first three quarters, went 5 of 9 from beyond the arc in the fourth.
The Pelicans pulled even at 65 on a layup by Davis with 1:23 left in the third period, but Morris scored the last six points of the quarter to take a 71-65 lead into the fourth.
"We just didn't have our best stuff tonight," Pelicans coach Monty Williams said. "You could complain about the whistles but that's not going to get you anywhere. We didn't make an effort to get to the basket. We fell in love with jump shots and didn't finish around the basket."
Dragic returned after missing three games with a sprained left ankle. ... Phoenix led 19-16 after the first quarter despite shooting 33.3 percent from the floor. ... Smith's 14 first-half points matched his full-game season high and he broke the 20-point mark for the fifth time in his career. .. Morrow was the only New Orleans player to score off the bench in the first half, scoring eight points while the Pelicans' other five bench players went 0 for 8 from the floor in 21 combined minutes. ... New Orleans didn't attempt a free throw in the first half. ... Bledsoe's four 20-plus point games match the total he had in 197 career games entering the season. ... Phoenix has won five straight at home.