Runs of 23 and 75 secured frame one and while O’Brien got his hand on the table first in frame two he could only muster breaks of 5 and 21 before Selby mopped up to take a two-frame advantage.
Selby secured scrappy frames three and four before a run of 76 in frame five ensured a whitewash and a place in the semi-final stage.
Top seed Ding Junhui raced into an early lead against Graeme Dott, wrapping up the opening two frames in quick succession before Dott stopped the rot with a break of 89.
Gibraltar Open
'Like a thunderbolt' - Lisowski wows with brilliant pot
However, breaks of 101 and 56 helped the Chinaman extend his lead and gave him the impetus to wrap up the win in style.
Joining Selby and Ding at the semi-final stage will be Mark Allen who prevailed 5-4 against Michael White.
Allen opened up a two-frame advantage courtesy of breaks of 83 and 55 but White responded with a 50 to cut the arrears.
However, a break of 74 secured frame four for Allen before he took a tactical fifth frame 67-55 to open up a 4-1 advantage.
White produced breaks of 85, 83 and 76 to level the match at four apiece but, with the initiative seemingly with White, Allen managed to grind out the decider 57-36.
Stuart Bingham also advanced into the last four with a relatively routine victory over Scot Alan McManus, winning the match by five frames to one.
Bingham led early on with a solid break followed by some very competent potting from around the table. However, McManus fought back in the second frame as he levelled the match.
That was all Bingham was to allow his opponent, though, as the Englishman sealed the following four frames to claim the win.
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Gibraltar Open
'An unbelievable shot' - Lisowski wows with brilliant red
Gibraltar Open
'Terrific pot' - Wilson drains stunning long pot