Malaga left it late to overcome Segunda Division side Eibar 4-1 and reach the Copa del Rey quarter-finals after a drawn first leg.
The Primera Division and Champions League outfit trailed for over an hour after Ruben Arroyo's 12th-minute goal put Eibar 2-1 up on aggregate, only drawing level in the 74th minute through Diego Buonanotte.
Seba Fernandez and Francisco Portillo then put them ahead and, after Eibar had substitute Guille Roldan sent off, Buonanotte scored again in added time to wrap up a 5-2 aggregate success.
Valencia also advanced to the last eight, beating Osasuna 2-1 at the Mestalla to complete a 4-1 aggregate win.
Tino Costa added to Los Che's first-leg advantage in the 36th minute and though Joseba Llorente responded within a minute, there was no way back for Osasuna and Roberto Soldado's last-minute goal rubbed salt in their wounds.
Parrish scored his first goal in more than 140 first-team appearances as Jim Bentley's side came from behind to record their first win in seven games.
The Shrimps got off to the worst possible start when they went a goal down after just six minutes. Matthew Saunders swung in a corner from the right which flew across the Morecambe penalty area before Brian Woodall produced a fine finish to volley past Barry Roche from 12 yards.
It was a goal that silenced the home crowd and the Daggers almost doubled their advantage after 15 minutes when Stewart Drummond headed towards his own goal forcing a vital clearance from Kevin Ellison.
Morecambe raised their game in the second half and levelled after 53 minutes with Jordan Burrow scoring his first goal of the season. Lewis Alessandra crossed to the far post and Ellison headed back into the danger area with Burrow in the right place at the right time to bundle the ball past Chris Lewington from close range.
Morecambe continued to attack the visitors and were denied a second with an excellent save from Lewington to tip away a sweetly-struck Ellison strike from the edge of the box.
Gary McDonald then saw a close-range volley superbly cleared off the line by Scott Doe before the Shrimps took the lead with 11 minutes to go when Parrish steamed in at the far post to force the ball over the line from close range after a superb run and cross from Alessandra.