Battling all odds, White came up a with a stunner of an innings that lifted Australia to 168 for five from a calamitous start after electing to bat.
White's crafty knock and his unbeaten 101-run partnership with Mike Hussey (39) snatched the initiative from the Sri Lankans, who had reduced the Australians to 67 for five.
Spinner Suraj Randiv was responsible for Australia's misery early on as he bowled a dream spell in which he took three wickets and conceded just 20 runs.
Sri Lanka's start, like Australia, was disastrous as they lost wickets in a heap but they could find a White like rescuer and were bowled out for a paltry 87 in 16.2 overs.
Australia are unconquered so far and the comprehensive win in today's encounter, which boosted their net run-rate (+3.25), have ensured their place in the semifinals.
Sri Lanka will now have to beat India on Tuesday and pray that Australia beat West Indies if they have to make the last-four stage.
In-form Mahela Jayawardene has been instrumental in his sides's smooth run so far in the tournament and his failure today impacted Sri Lanka's performance.
Also, the Australian fast bowlers yet again were clinical with Mitchell Johnson (3/15) and Dirk Nannes (2/19) sharing five wickets.
Jayawardene (9) fell immediately after hitting Nannes for a six and soon Sri Lanka were three for 26 as yet again Aussie pacers spit fire.
Tillakaratane Dilshan (20) and Angelo Mathews tried to put up some fight, hitting Shane Watson for 15 runs in the sixth over but Johnson removed both in the next over.
Dinesh Chandimal (19) was the other batsman to manage a double-digit score and his dismissal, a stumping off Steven Smith (2/13), ended all Lankan hopes.
Earlier, Randiv rocked the Australia middle-order before White scored a masterly half-century to rescue his side.
Electing to bat, Australia were in an unusually pathetic situation of having lost four wickets at a score of 33 and were reduced to 67 for five in 11 overs but White brought his side back in the match.
White made Sri Lanka pay heavily for dropping him, when he was on 23 in 11th over, and raised the match winning partnership with Mike Hussey.
Sri Lanka were all over Australia after Randiv's super spell but White killed the Lankan joy with his bludgeoning innings, adorned with six fours and as many sixes.
His fiery 49-ball knock helped Australia muster 69 runs in the last five overs and go into the defence of the total with momentum.
White was going hammer and tongs while Mike Hussey, the ever reliable, supported him by rotating the strike.
Sri Lankan bowlers undid all the good work done at the start as they were hammered around all round the park.
Australia, who have looked so far the most dangerous side in the tournament, were off to a shocking start after winning the toss as their top-order collapsed.
Kumar Sangakkara made some intelligent moves and his bowlers -- both pacers and spinners -- responded well as they were spot with their line and length.
Angelo Mathews did not have fearsome pace but was rewarded for his persistence on the off-side as he removed dangerous Shane Watson (1) and Brad Haddin (15) in successive overs to give his side a fabulous start.
Randiv, drafted into final-XI today, made sure that his side does not feel the absence of Muttiah Muralitharan as he bowled a sensational first over, scalping David Warner (9) and David Hussey (0) off successive balls.
While Warner was out in the slip region, Hussey was stumped by Sangakkara after being foxed by the line.
Michael Clarke became the third victim of Randiv just two balls after Mendis dropped White.
Score Board
Australia
S Watson b Mathews 1
D Warner c Jayawardene b Mathews 9
B Haddin c Jayasuriya b Randiv 15
M Clarke b Randiv 14
D Hussey st Sangakkara b Randiv 0
C White not out 85
M Hussey not out 39
Extras: (LB-2, Wd-1, NB-2) 5
Total: (for five wkts in 20 overs) 168
Fall of wicket: 1-2, 2-20, 3-30, 4-30, 5-67.
Bowling: A Mathews 4-0-24-2, C Welegedara 4-0-40-0, S Randiv 4-0-20-3, L Malinga 4-0-40-0, A Mendis 4-0-42-0.
Sri Lanka
M Jayawardene c Smith b Nannes 9
S Jayasuriya lbw b Nannes 5
K Sangakkara c Haddin b Tait 2
T Dilshan c White b Johnson 20
A Mathews c M Husseyb Johnson 8
D Chandimal st Haddin b Smith 19
C Kapugedera b Smith 12
S Randiv run out 2
L Malinga c Smith b Clarke 1
A Mendis b Johnson 1
C Welegedara not out 2
Extras (lb-2, wd-4) 6
Total (all out in 16.2 overs) 87
Fall of wickets: 1-16, 2-18, 3-26, 4-48, 5-49, 6-73, 7-83 8-83, 9-84.
Bowling: D Nannes 3-0-19-2, S Tait 2-0-10-1, S Watson 3-0-27-0, M Johnson 3.2-0-15-3, S Smith 4-1-12-2, M Clarke 1-0-2-1.