European benchmark London Brent North Sea oil jumped to a new three-year peak at $82.72 per barrel.
New York crude zoomed to a fresh seven-year pinnacle at $78.88.
OPEC and other major producers opted Monday against increasing output by more than previously agreed -- despite tightening supplies and rising demand.
The OPEC+ grouping decided to stick with their planned increase next month in oil production of 400,000 barrels.
"OPEC+ gave oil bulls a red rag to bid up futures contracts as it stuck to the planned increase," said Markets.com analyst Neil Wilson.
"It's not that demand is suddenly forecast to improve -- it's more that OPEC+ is keeping such a tight grip on supply."
Runaway oil prices fuel higher inflation but boost the profits and revenues of energy giants.
In London, BP shares rose 0.6 per cent to 346.45 pence and Royal Dutch Shell's 'B' shares jumped 1.3 per cent to £16.93.
In Paris, France's Total rallied 1.8 per cent to 42.83 euros, and in New York shares in ExxonMobil climbed 1.1 per cent to $62.40.
"OPEC's decision not to lift production volumes gave oil prices a lift into Tuesday, helping the FTSE 100 to solid gains as index heavyweights BP and Shell gushed higher," said AJ Bell investment director Russ Mould.
Wall Street rebounded at the start of trading, shaking off losses on Monday over concerns about the impact of higher energy prices on economic growth and the ongoing standoff in Washington over raising the country's borrowing limit, which has fuelled fears of a catastrophic US debt default.
"It remains to be seen whether the bulls will be able to hold their ground in the face of rising concerns over stagflation," said ThinkMarkets analyst Fawad Razaqzada.
Elsewhere on Tuesday, most Asian markets fell following a Wall Street's Monday slump as surging oil prices also put further upward pressure on inflation.
Investors were nervously monitoring developments in the crisis surrounding troubled property giant China Evergrande, which has raised warnings about contagion in the world's number two economy and possibly beyond.