Erik ten Hag's side were in control for large parts of the first period, as Fernandes netted his fifth goal of the season, latching onto a clever pass from Christian Eriksen to open the scoring.
But Olise's superbly placed set piece, deep into stoppage time, ensured a share of the spoils in the capital as the Reds' nine-match winning run came to an end.
Brazilian midfielder Casemiro was shown his fifth yellow card of the season for a foul on Wilfried Zaha, and will therefore now miss Sunday's clash with Arsenal at the Emirates Stadium.
Despite the frustration caused by the late equaliser for our opponents, there were still plenty of impressive performers on duty for United.