Murray recovered from losing the first three games of the match to come through 6-4 6-3 in an hour and 35 minutes against the world No 116.
Murray played a fairly decent match to take down a player that can be tricky to beat. Murray had many issues with O'Connell earlier this year but was able to beat him in a simpler fashion this time around. Up next for him is Alexander Bublik. Murray has won two of his three previous matches against Kazakh Bublik but lost their most recent clash in Indian Wells in March.
He said:
"I just want to keep improving week on week and match on match. That's all you can do really. You can't control the results, you can't predict how the results are going to go but hopefully I can make improvements each round."