Seemingly unaffected by his ailing right knee that was drained of fluid last week, Bryant choreographed a stunning display by the Lakers as they made the most of their size advantage against the smaller but speedy Suns.
The All-Star guard, who shot 13-of-23 from the field, scored 21 points in the third quarter alone to help his team tighten their grip after Phoenix had made a fast start at the Staples Center.
Spanish forward Pau Gasol added 21 points and Ron Artest 14 while Lamar Odom, off the bench, weighed in with 19 points and a playoff career-high 19 rebounds for the top seeds.
Forward Amar'e Stoudemire led the Suns with 23 points and guard Jason Richardson contributed 15.
Watched by a capacity crowd of 19,000 that included actors Dustin Hoffman and Sylvester Stallone, the Lakers were virtually unstoppable for the last two quarters as they won their seventh successive game in the playoffs.
"This is a surprise for us," Lakers head coach Phil Jackson told reporters. "We thought this was going to be a close game and we were able to jump away from them in the third quarter.
"Kobe had an outstanding night. He carried a lot of the offense. Pau played a fine game and so did Lamar. His rebounding in the second half was very instrumental."
APPLAUDED DISPLAY
Phoenix guard Steve Nash, who was restricted to 13 points by the Lakers, applauded the display by Bryant who completed the 11th game of his playoff career with at least 40 points.
"He had it going," the Suns guard said. "I didn't feel like we sent him to the (free throw) line a ton, I didn't feel like we let him get inside a ton but he made a ton of shots.
"You've got to tip your hat to the kind of performance he put on out there tonight."
The third-seeded Suns made a promising start by racing from 7-0 up into an early 22-17 lead before the Lakers fought back. Reserve forward Odom swiftly added seven points to help the home team lead 35-26 after the first quarter.
The Lakers maintained control in the second period, briefly forging 11 points clear after an Odom two-pointer before grabbing a 62-55 advantage by half-time.
Bryant and Gasol caught fire in the third quarter, the highlight coming when they combined superbly for a Bryant slam dunk that put Los Angeles 17 points ahead to send the crowd into a frenzy.
The Lakers took a commanding 93-79 lead into the final period and never relinquished their grip as they continued to make the most of their size advantage with a powerful inside game.
"They played great, one of the best games I've seen them play in the playoffs this season," Suns coach Alvin Gentry said.
"Kobe kind of controlled the whole game. We've just got to do a better job on the points in the paint."
Game Two, also at the Staples Center, will be on Wednesday.