That goal maintained Victory's record of only suffering one defeat on the road this campaign, but Thompson's goal wasn't enough to take his team to the top of the A-League table.
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It was the home side who started the match on the front foot, but with nine minutes gone, Victory took the lead when Ben Khalfallah found the back of the net from the edge of the area.
Moments later, Adelaide attempted to hit back through James Jeggo but his speculative effort was well kept out by Nathan Coe, before Sergio Cirio just missed the target after being set up by Nigel Boogard.
United continued to dominated proceedings, and shortly before the break, they got their reward when Pablo Sanchez rose above the defence to head home.
The opening stages of the second period were lacking in clear-cut opportunities, but Adelaide continued to have the better of possession and with 16 minutes left, they edged in front when Dylan McGowan powered home a header from close range.
However, it took Victory just three minutes to get back on level terms through Thompson, who drifted in between the defence before rounding the goalkeeper and tapping home into an empty net.
Back came Adelaide, who saw Jeggo denied by another impressive intervention from Coe, but the score remained the same as both teams missed out on the chance to move to the top of the A-League standings.