Randolph had 25 points and 19 rebounds and the Grizzlies defeated the Jazz 86-70 on Wednesday night, eliminating Utah and assuring the Los Angeles Lakers of a playoff spot even before their late game against the Houston Rockets.
Meanwhile, Memphis, the Western Conference's fifth seed, still held hopes for home-court advantage. But the Los Angeles Clippers' 112-108 victory over the Sacramento Kings on Wednesday night means the series will open this weekend in Los Angeles.
The series will be a repeat of last year's Western Conference opening-round series won by the Clippers in seven games, despite Memphis holding home-court advantage.
Randolph looked like the player who made the All-Star team this season and led the Grizzlies to the second round of the playoffs two years ago.
He seemed quicker to the basket than in recent games and worked hard to get to the rim and on the boards.
"I just tried to be aggressive," said Randolph, who had averaged 12 points and 9.4 rebounds in the past five games.
"It's a new season, and I want to go in with confidence up and try to play the way I usually play.
"Tonight was a good night for me, and now I just need to carry on to a new season."
Al Jefferson scored 22 points and grabbed 16 rebounds to lead Utah, the only Jazz player in double figures.
The Jazz managed only 32 percent shooting and were outrebounded 57-47 in a game they needed to win to capture the last Western Conference playoff spot.
A sporadic third quarter, where the Jazz were outscored 25-13 was Utah's undoing.
"It's disappointing anytime you don't make the playoffs," Utah coach Tyrone Corbin said. "That was the goal we set at the beginning of the year. It's always disappointing when you don't go. We had an opportunity, but didn't get it done."
Randolph ended the third quarter with 12 points and seven rebounds as Memphis built the advantage to 16 before carrying a 65-51 lead into the fourth.
"The third quarter hurt us," Jefferson said. "I think we played good besides the third quarter. .We took a lot of great shots that we normally hit. It just didn't go in for us."
The Grizzlies built the lead to 20 in the early part of the fourth.
Utah made one more push, cutting into the Memphis advantage with eight straight points, part of a 12-2 Jazz run.
That reduced the Grizzlies' lead to 75-65 with just under 5 minutes left, but the Jazz never got closer.
"They slowed the ball up. They pounded it inside," Jazz forward Paul Millsap said of the Grizzlies. " ... It was tough for us to climb back up that hill. We just couldn't get over it."
The start of the game seemed to lack the intensity of two teams with playoff implications.
About 10 minutes in, the Jazz were shooting 25 percent, while Memphis was at 37 percent. The Grizzlies' starting front-line opened the game missing 10 of 13 shots.
The shooting eventually got a tad better, but both were under 41 percent at the half as the Grizzlies carried a 40-38 lead into the break.
Jefferson was the only player in double figures with 10 points, while Randolph led the Grizzlies with eight points and eight rebounds.
The defense picked up a bit in the third, but the Jazz's shooting woes continued as Utah missed its first six shots, en route to hitting only 3 of 14, while Memphis built the lead to double digits.
Utah finished the third hitting 4 of 18 shots and committing four turnovers.
It was Randolph who took control for Memphis, working inside and grabbing rebounds. Conley was providing a nice supporting role, taking the ball to the rim.
"(Randolph) was outstanding," Memphis coach Lionel Hollins said. "He missed about five layups, but he went back and got them. I thought he was super aggressive.
"He looked like he was mentally into the game. He hasn't been the last few games, but he was (against the Jazz). I would say that he is in playoff mode."
The home victory was Memphis' 32nd of the season, a franchise record. ... Randolph came up limping in the first half after twisting his right ankle, but played through it. The Grizzlies forward missed four games in March after rolling his left ankle. .The Jazz had a team dinner Tuesday night at a local Memphis restaurant. "It was a combination of the guys getting together, knowing and understanding that we're together, and want to stay together for a little while longer," in the postseason, Jazz coach Tyrone Corbin said before the game. ... The Grizzlies announced earlier in the day that they have signed Donte Greene and Willie Reed. Both were inactive for the game. ... As sports teams have done across the country, there was a moment of silence before the game for the victims of Monday's bombings in Boston.