The Jazz appear to have an easier schedule down the stretch than the Lakers, who must visit the Clippers and Portland while also hosting playoff-bound San Antonio, Golden State and Houston.
Nash missed his second straight game with hamstring problems, while World Peace is out following knee surgery. Until the final seconds, Conley dominated his matchup with Nash's replacement, Steve Blake, who had six points and five turnovers.
The teams traded the lead down the stretch of a tense fourth quarter. Randolph's jumper with 2:32 left put the Grizzlies up 84-83, but Bryant fed Gasol for a driving layup with 1:36 to play to put the Lakers back ahead.
After Jerryd Bayless missed an open shot, Los Angeles took roughly a full minute off the clock with an offensive rebound and another miss that went out of bounds off the Grizzlies. Bryant missed a 20-footer with 17 seconds left, but Conley missed an open jumper.
Howard grabbed a one-armed rebound while getting fouled, and the All-Star center made one of two free throws. Memphis went right back to Conley, but his twisting drive into the lane didn't produce any points or a foul.
"We executed like we were supposed to, and tried to get a shot up," Conley said. "We tried to get some penetration and see what we can make out of it, but it just didn't work out."
Bryant sat out just 79 combined seconds of the past two games while pushing the desperate Lakers to victories, even racking up his 19th triple-double Tuesday against Dallas. With an afternoon game against the Clippers looming on Sunday, played a mere 42:32 against the Grizzlies.
NOTES: With his first basket against Memphis, Bryant broke his sixth-place tie with Elvin Hayes in NBA history with the 10,977th field goal of his 17-season career. ... More than five years after his departure for Los Angeles, Pau Gasol is still the Grizzlies' franchise career leader in points, rebounds and blocked shots. ... Marc Gasol got a personal foul and a technical foul for arguing in the second quarter after he appeared to clip his brother in the head with an accidental elbow.