Adelaide lost 5-25 in that match-defining period, before MacGill cleaned up with 2-12 from four wily overs.
The Strikers' gun openers Michael Klinger (duck) and Daniel Harris (nine) were silenced and their mid-order misfired without Callum Ferguson, who was axed after 38 runs in five games.
Left-hander Aiden Blizzard loomed dangerous with 27 from 21 balls but inexplicably popped the softest of catches to wide mid-on.
Blizzard was the only of Adelaide's top six batsmen into double-figures, with Adam Crosthwaite the second-highest scorer with 13.
Earlier, Adelaide contained the Sixers to 8-151 from 20 overs with imported paceman Alfonso Thomas a stand-out.
The South African claimed 3-24 while Brendan Drew (1-26), Daniel Salpietro (1-28) and Aaron O'Brien (0-26) delivered tidy four over stints.
Moises Henriques top scored with 42 from 37 but, like his team-mates, was largely unable to break free of tight bowling.
First drop Nic Maddinson was at ease in making 31 from 20 balls before slicing to point and McCullum (20 not out from 19 balls) was next best.
The Sixers lost 4-23 in a middle order slump of their own but their bowling brigade covered for a win which took them to eight competition points - the same as leaders Hobart Hurricanes and Perth Scorchers.
Adelaide Strikers captain Michael Klinger apologised to the crowd, and his bowlers, for the weak batting display.
"Our top seven (batsmen) owe a lot of apologies,'' Klinger said.
"It seemed like any semi-risk we took, we got out.''
Sydney Sixers' man of the match O'Keefe was rapt with the blow-out margin.
"I guess in Twenty20 matches, they can go that way if you get on top early, like we did,'' O'Keefe said.
"We weren't expecting to roll them for 87 at all.''
- AAP
