Home skipper Richard Naylor headed into his own net to put Millwall ahead in the 15th minute but Grayson's men levelled through Lloyd Sam's 32nd-minute strike before going on to dominate much of the game.
They looked to be left frustrated until Johannesburg-born Somma, 25, edged Leeds ahead in the 79th minute before adding gloss to a deserved victory with a brilliant finish in added time.
Somma arrived at Elland Road last summer from America's MLS before being sent out on loan to Chesterfield and Lincoln last season to learn his trade.
His nine goals in 14 games helped the Imps to avoid relegation and his cameo against Millwall on his first start for Leeds suggested he can perform regularly in the second tier of English football.
"We decided to bring Davide in on trial, we liked what we saw and offered him a contract," said Grayson. "He needed to adapt to English football, hence him going to Chesterfield first where he had a bit of a bad time.
"He then went to Lincoln where he had a successful time and now we've obviously reaped the rewards. Did I know he could he do it at this level? We were unsure but we knew he was a goalscorer and when you watch him in training he's got fantastic feet and is really composed. I want people coming in to make us even stronger and Davide Somma has certainly given me something to think about."
Source: PA
Source: PA