Johnson finished with 4/19 and Tait, bowling in short spells, took 2/34 as defending champions Australia dismissed Zimbabwe for 171 after scoring a challenging 262/6 in the day-night match.
There was no respite from pace for the hapless Zimbabwe as Brett Lee also tested the batsmen to finish with 1/34 as Australia continued their winning streak in the World Cup.
The win was also the perfect way for captain Ricky Ponting to celebrate his record-breaking 40th World Cup match in the Group A clash at the Sardar Patel Gujarat Stadium.
Australia, aiming to win a fourth successive World Cup, virtually wrapped up the match when they reduced Zimbabwe to 44/4 in 12.3 overs, with Johnson taking two wickets and Lee and Tait one apiece.
Zimbabwe, however, had reasons to be pleased with the performance of their spinners, who did not allow the Australian batsmen to score freely with their disciplined efforts.
But their top-order batsmen failed to back the bowlers, offering no resistance to the Australian pace trio of Johnson, Tait and Lee with tailender Graeme Cremer top-scoring with a fighting 37.
Lee was the first to strike when he removed Charles Coventry, who top-edged an attempted pull to be caught by the bowler. The Zimbabwean made 14, including a flat six over point off Lee.
Johnson had Tatenda Taibu caught by Shane Watson in the slips and trapped Craig Ervine lbw in successive overs, while Tait bowled Brendan Taylor before accounting for Sean Williams (28).
Australia were earlier indebted to in-form opener, and man of the match, Watson (79) and Michael Clarke (58 not out) for setting a challenging target, but could never really dominate the Zimbabwean spin attack.
Zimbabwe used seven bowlers, including five spinners who sent down 39 of the allotted 50 overs.
Left-arm spinner Price, who shared the new ball with seamer Christopher Mpofu, was instrumental in keeping the run-rate low early in the innings with a tidy line and length to finish with 1/43 off 10 overs.
Off-spinner Prosper Utseya and leg-spinner Cremer bagged one wicket apiece, giving away 84 runs in a combined tally of 20 overs.
Watson, who smashed one six and eight fours in a 92-ball knock, added 61 for the opening wicket with Brad Haddin (29) and 79 for the next with Ponting (28).
Clarke provided the late flourish with a 55-ball knock as Australia plundered 90 runs in the closing 10 overs, with Cameron White (22), David Hussey (14) and Steven Smith (11) playing supporting roles.
Australia managed just 65 in the opening 20 overs, their best coming when Watson and Haddin smashed two fours apiece in a Mpofu over in a rare show of aggression.
Skipper Elton Chigumbura promptly turned to spin.
Utseya provided the breakthrough when he trapped Haddin lbw, with Zimbabwe asking for a review of the umpire’s decision after the batsman had initially been given not out.
Watson was also ruled out lbw off Cremer following a referral, but not before he had set the stage for the final onslaught.
Ponting looked set when he was run out after a superb piece of fielding by Mpofu, who hit the stumps at the non-striker’s end from deep midwicket. Khaama Press (KP).