By Dmitry Zhdannikov, Rania El Gamal and Reem Shamseddine

VIENNA (Reuters) - Russian oil billionaire Vagit Alekperov isn't easily swayed, but Saudi Arabia's new Energy Minister Khalid al-Falih achieved it this week.

Intense diplomacy by the soft-spoken Falih at his first OPEC meeting - with his speech peppered by words such as "gentle approach", "no shocks" and "consensus" - has persuaded Alekperov that OPEC is more alive than dead.

"The fact that OPEC agreed on its new management shows they want to regain their coordinating role. The cartel will perform market management again," Alekperov, chief executive of Russian energy firm Lukoil, said after meeting Falih and Iranian Oil Minister Bijan Zanganeh separately in Vienna.

On Thursday, OPEC could not agree to set a clear oil-output target as Iran refused to limit its own production.

But the meeting was relatively peaceful and free of the usual clashes between political rivals Saudi Arabia and Iran, with Falih promising not to flood the market and to listen to Tehran.

In a rare compromise, OPEC also decided unanimously to appoint Nigeria's Mohammed Barkindo as its new secretary-general after years of friction over the issue. Oil prices stood flat at $50 a barrel on Friday, up 80 percent from their January lows.

Falih, who in April succeeded veteran Ali al-Naimi, was the first OPEC minister to arrive in Vienna.

He met most fellow colleagues on the sidelines, spent several hours with independent OPEC analysts and held a long news conference with reporters.

"If you want to call it (OPEC) a talking shop - I have no problem with that. But I think it's going to do a lot more than talking. We are going to do coordination and cooperation ... to achieve market objectives," Falih said on Thursday.

DRIVERLESS CAR

The nature of Thursday's meeting surprised many OPEC watchers, who have grown used to acrimonious gatherings.

Falih's ultimate boss, Saudi Deputy Crown Prince Mohammad bin Salman, effectively scuppered plans to clinch a global production freeze in the Qatari capital of Doha in April.

Prince Mohammad said Riyadh would not agree to the deal, which would also have involved non-OPEC Russia, if Iran didn't join in despite Tehran insisting it wants to regain market share after the lifting of international sanctions earlier this year.

"After Doha, oil markets were beginning to look like a driverless car. That needed to change," said a source familiar with Saudi thinking.

A non-Gulf OPEC source said Riyadh realized it needed OPEC unity because the group's fight for market share against higher-cost producers, such as U.S. shale, was taking longer than expected when formulated in 2014.

"The Saudis trashed OPEC in Doha. But they realized they don't want to throw away decades of OPEC history and decided to be more cooperative," said Gary Ross, founder of U.S.-based Pira consultancy, who came to Vienna together with other OPEC watchers and analysts for meetings.

"The Saudis definitely decided to change tack after Doha as they were concerned that people were doubting the viability of OPEC. I think this softer approach will last," said Amrita Sen, who also came to Vienna.

Falih acknowledges that Riyadh realized it needs OPEC.

"The markets can ultimately balance themselves but as we have seen, when we rely on markets alone it is extremely painful for everybody," he said on Thursday.

"I think managing in the traditional way that we have tried in the past may never come again ... We will not go with setting a price target for OPEC ... But (we should be) coordinating strategies and trying to understand what each of us can and cannot do."

(Additional reporting by Alex Lawler and Shadia Nasralla; Writing by Dmitry Zhdannikov; Editing by Dale Hudson; Editing by Dale Hudson)