Pompey made a breakthrough after nine minutes, when a headed pass to Colby Bishop rebounded off his leg to Anderson, who took a smart touch to his left before firing his side into the lead.
The shot flew into the net via keeper Jamie Cumming, who got a hand to the effort but could not keep it out.
Pompey’s momentum was then halted when referee Josh Smith produced a straight red card for Ogilvie after a heavy touch forced him to lunge for the ball, catching Mills from behind in the process.
The hosts then had a brilliant chance to double their lead when Jordan Williams played a low cross to Gustavo Caballero in a great position from the left, but he blasted over the bar.
Oxford managed to find a leveller when Mills struck from outside the box and Schmid’s save was pushed to Spencer, who was able to divert the ball home.
Plenty of abuse from the home fans was directed towards the referee in the second half because of the red card handed to Ogilvie.
Every foul and decision had them on their feet, which made for a chaotic and breathless affair on the pitch.
Oxford went ahead when Helik swung a delightful cross to the back post, where Lankshear threw himself at the ball and powered it into the top-right corner with a diving header.
But Portsmouth refused to lie down and substitute Alli made a dart down the left and crossed first time to Dozzell, who calmly slotted into the bottom right corner of the net.