Gold prices also rose back towards a record high thanks to a rush into safe havens, but equities were mixed amid hopes that the conflict does not spread through the Middle East.
Investors were also gearing up for key central bank meetings this week, with a particular eye on the US Federal Reserve and Bank of Japan, as well as talks with Washington aimed at avoiding Donald Trump's sky-high tariffs.
Israel's surprise strike against Iranian military and nuclear sites on Friday -- killing top commanders and scientists -- sent crude prices soaring as much as 13 percent at one point on fears about supplies from the region.
Analysts also warned that the spike could send inflation surging globally again, dealing a blow to long-running efforts by governments and central banks to get it under control and fanning concerns about the impact on already fragile economies.
"The knock-on impact of higher energy prices is that they will slow growth and cause headline inflation to rise," said Tony Sycamore, a market analyst at IG.
"While central banks would prefer to overlook a temporary spike in energy prices, if they remain elevated for a long period, it may feed through into higher core inflation as businesses pass on higher transport and production costs.
"This would hamper central banks' ability to cut interest rates to cushion the anticipated growth slowdown from President Trump's tariffs, which adds another variable for the Fed to consider when it meets to discuss interest rates this week."
Both main oil contracts were up around one percent in Asian trade.
- Fed, BoJ in focus -
But Morningstar director of equity research Allen Good said: "Oil markets remain amply supplied with OPEC set on increasing production and demand soft. US production growth has been slowing, but could rebound in the face of sustained higher prices.
"Meanwhile, a larger war is unlikely. The Trump administration has already stated it remains committed to talks with Iran.
"Ultimately, fundamentals will dictate price, and they do not suggest much higher prices are necessary. Although the global risk premium could rise, keeping prices moderately higher than where they've been much of the year."
Tokyo closed 1.3 percent higher, boosted by a weaker yen, while Hong Kong reversed early losses and Shanghai, Seoul, Singapore and Wellington also advanced.
Taipei, Jakarta and Manila retreated while Sydney was flat.
London, Paris and Frankfurt were all higher in early trade.
Gold, a go-to asset in times of uncertainty and volatility, rose to around $3,450 an ounce and close to its all-time high of $3,500.
There was little major reaction to data showing China's factory output grew slower than expected last month as trade war pressures bit, while retail sales topped forecasts.
Also in focus is the Group of Seven summit in the Canadian Rockies, which kicked off Sunday, where the Middle East crisis will be discussed along with trade in light of Trump's tariff blitz.
Investors are also awaiting bank policy meetings, with the Fed and BoJ the standouts.
Both are expected to stand pat for now but traders will be keeping a close watch on their statements for an idea about the plans for interest rates, with US officials under pressure from Trump to cut.
The Fed meeting "will naturally get the greatest degree of market focus", said Chris Weston at Pepperstone.
"The Fed should remain sufficiently constrained by the many uncertainties to offer anything truly market-moving and the statement should stress that policy is in a sound place for now," he added.
In corporate news, Nippon Steel rose more than three percent after Trump on Friday signed an executive order approving its $14.9 billion merger with US Steel, bringing an end to the long-running saga.
- Key figures at around 0715 GMT -
West Texas Intermediate: UP 1.1 percent at $73.81 per barrel
Brent North Sea Crude: UP 0.9 percent at $74.93 per barrel
Tokyo - Nikkei 225: UP 1.3 percent at 38,311.33 (close)
Hong Kong - Hang Seng Index: UP 0.8 percent at 24,077.01
Shanghai - Composite: UP 0.4 percent at 3,388.73 (close)
London - FTSE 100: UP 0.2 percent at 8,866.0
Euro/dollar: UP at $1.1572 from $1.1540 on Friday
Pound/dollar: UP at $1.3584 from $1.3560
Dollar/yen: UP at 144.27 yen from 144.04 yen
Euro/pound: UP at 85.19 pence from 85.11 pence
New York - Dow: DOWN 1.8 percent at 42,197.79 (close)
London - FTSE 100: DOWN 0.4 percent at 8,850.63 (close)
dan/mtp/ecl
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