Saints took the lead in the 30th minute after Jack Stephens left Fernandes in a heap on the right.
Saints went into half-time 1-0 ahead, with the Premier League changing the award of the opening goal from Adams to a Fred own goal.
Fred deflected a Che Adams effort into David de Gea’s net to put Southampton a goal up.
United continued strongly as they pushed to take the lead on the south coast.
Greenwood levelled after the break to ensure United matched Arsenal’s Premier League record of unbeaten away games.
Pogba poked a Fernandes ball on to Greenwood, whose shot beat Alex McCarthy and found the back of the net in front of the raucous travelling support.
Armstrong sent over a smart cross and Tino Livramento lashed over for the hosts before United levelled in the 55th minute.