Emma Stone Dating Spider-Man Costar Andrew Garfield!

 Evan Agostini/MTV/PictureGroup

Web-slinging sweethearts!

Production on The Amazing Spider-Man wrapped in May, but the love story between costars Emma Stone, 22, and Andrew Garfield, 27, is far from over.

"They got close during filming and have been hooking up," a source tells the new issue of Us Weekly (on stands now). The new couple decided to keep things quiet, the source adds, because Garfield split with his girlfriend of three years, Raising Hope actress Shannon Woodward, in May.

(Stone recently parted ways with Kieran Culkin, 28, her beau since last fall.) "They haven't gone public, but he's told his friends," the insider says.

Sparks definitely flew between the costars at the MTV Movie Awards on June 5. First, the pair flirted throughout the ceremony (he was seated behind her). Then, at the afterparty, she squealed when she saw him — and they chatted for another 20 minutes!

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