Johnson's innings and Australia captain Ricky Ponting's 79 took Australia to 275-8. Nathan Hauritz, Shane Watson and Peter Siddle then all took two wickets to bowl out West Indies for 225 with 19 balls remaining at Wanderers Stadium.
"Mitchell played exceptionally well and he showed how dangerous he can be during the batting powerplay," Ponting said.
Johnson didn't take a wicket with his hostile fast bowling, but he ran out opening batsman Andre Fletcher for 54 to break a threatening 86-run partnership for the third wicket with Travis Dowlin (55).
Australia sent down 16 wide deliveries. Brett Lee was the chief offender with six, and Johnson had four.
"We didn't bowl at our best as we gave away too many extras," Ponting said.
West Indies set out promisingly in pursuit of the target, with Fletcher and Dowlin taking the team to 124 by the 25th over. But neither batsman was able to push on and increase the scoring rate.
"One of the batsmen needed to carry on and get a big score," West Indies captain Floyd Reifer said.
West Indies' challenge petered out as the run-rate required ballooned without the batsmen capable of hitting boundaries. West Indies No. 11 Dale Richards was unable to bat after he dislocated his shoulder while fielding.
For Australia, Johnson hit eight fours and three sixes in recording his highest one-day international score. He shared in a 70-run partnership for the eighth wicket with Lee during a batting powerplay from the 44th to the 48th over.
Lee contributed only 25 of those runs as Johnson manufactured some innovative shots, mixed with raw power in smashing three sixes over the midwicket boundary at Wanderers.
Australia got off to the worst possible start with Shane Watson bowled off the opening ball of the innings by Kemar Roach. But Ponting steadied the innings on a pitch that contained plenty of bounce.
Ponting hit 79 off 94 balls with 11 fours and a six, and had to survive at least three deliveries that jumped up off a length and hit him on his gloves or torso.
West Indies' bowlers did well after Ponting and Tim Paine (33) had put on 85 for the second wicket as Australia lost 5-86 with wickets falling at regular intervals. Callum Ferguson made 20 to be the only other batsman to reach double figures.
Left-arm spinner Nikita Miller was largely responsible for the tight bowling, taking 2-24 off 20 overs. He had Ponting stumped, and bowled the dangerous Cameron White for 4.
"Johnson played a magnificent innings," Reifer said. "Our guys bowled well in the beginning, but once he got going there wasn't much we could do."
