It looked as though Adelaide was on its way to a second loss in four games, as Bobo rounded off a lovely move to open the scoring in the 19th minute, before doubling his tally early in the second half with a simple finish into an empty net after Kosta Barbarouses wasted a one-on-one situation.
But United pulled one back 15 minutes from time, Jordan Elsey turning in a left-wing cross, and Tomi Juric's fierce strike a few moments later restored parity.
Adelaide might have gone on to seal the win and subsequently leap above Melbourne City, who went top on Saturday with a remarkable 7-0 derby win over Melbourne Victory, but Rhyan Grant brought Craig Goodwin down as the last man to earn a straight red deep into stoppage time.
Just outside Sydney, Macarthur was held to a 2-2 draw by the Newcastle Jets, whose club-record winless streak was extended to eight games.
But just as they did last week against Perth Glory, the Jets showed character to fight back from behind, with Charles M'Mombwa and Loic Puyo putting Macarthur 2-1 up after Roy O'Donovan's penalty had initially put the visitors in front.
Steven Ugarkovic equalised just before the hour mark with a gorgeous 20-yard effort and that ultimately salvaged a point.
The day's late game was similarly entertaining and did yield a winner as Wellington Phoenix beat Glory 3-1, with all goals coming in the second half.
Ben Waine caught Glory goalkeeper Luke Reddy out of his net for the first, only for Joel Chianese to equalise two minutes later with a stunning effort, picking out the top-left corner after slaloming between a couple of defenders.
But Louis Fenton tapped in to make it 2-1 with 66 on the clock and Jaushua Sotirio - released by the lively Ulises Davila - showed great composure to seal the win and boost the Phoenix's outside chances of reaching the Finals.