UPDATE 1-Peru poll shows Humala, Fujimori in virtual tie

* Fujimori closes gap with first-round winner Humala
* Nearly a fifth of voters undecided, planning to abstain (Updates with poll details, context)

LIMA May 7 (Reuters) - Peru's left-wing nationalist Ollanta Humala and right-wing lawmaker Keiko Fujimori are running almost neck-and-neck ahead of a June 5 presidential run-off election, a poll by Lima's Catholic University showed on Saturday.

The nationwide poll showed 40.7 percent of voters backed Humala while 40.5 percent supported Fujimori, with 18.7 percent of respondents still undecided or saying they would not vote for either.

Both candidates are courting moderate voters, who political analysts say will decide the election.

Peru's stock index .IGRA gained 10.88 percent last week after three other polls also said Fujimori, who has a graduate business degree from Columbia University in New York, had gained to a virtual tie.

Humala, a former army officer, campaigns as a moderate in favor of free market economic policies in the style of former Brazilian President Luis Inacio Lula da Silva, but he has faced mounting skepticism for discrepancies in his public statements and his official campaign platform.

Most recently, he pledged not to touch Peru's $30 billion in privately run pension funds.

Fujimori, 35, has closed the gap in polls since finishing 8 points behind Humala in the first-round vote on April 10 as she tries to distance herself from her father, jailed former President Albert Fujimori.

But many Peruvians have not forgiven her father for corruption and human rights abuses that marred the end of his 10-year rule.

Saturday's poll of 1,570 people, the Catholic University's first on the run-off, was conducted from April 30 to May 3 and has a margin of error of 2.47 percentage points. Polls from Ipsos Apoyo and Datum consultancy are expected on Sunday.