Sunderland closed the gap to leaders Rotherham United to three points with the 1-0 win at the Kassam Stadium, Jordan Willis' header from a Chris Maguire corner sealing victory over Oxford United.
Both sides had to contend with heavy rain and gales of up to 52MPH as Storm Dennis battered the country.
Sunderland also had to withstand a second half storm from the Oxford attack but they held firm with some resolute defending, recording their third clean sheet this week and seventh since the turn of the year.
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Parkinson said: “It’s the whole team, defending starts from the front, there were some heroic headers out the box from Charlie Wyke, Tom Flanagan - everybody played their part.
“We showed a strong character, our mentality was strong, concentration levels were great and we dug deep and had to. Conditions were tough. Oxford are a good team and have a lot of talent.
“It was a real team performance and I am so pleased with the points.
“Set plays are important and I was pleased Jordan got on the end of it - we couldn’t have wished for a better start.
“They have as many attacking options as any other team in the league, they are a good side and we had to be at our best in terms of organisation.
“The basic stuff, had to be right. The biggest cheer was when Denver [Hume] put himself on the line to stop a cross coming in.
It has to be everyone doing it and we certainly showed that.”
Parkinson also praised sub Josh Scowen, the January signing helping seal victory when he came on after an hour, with Kyle Lafferty and Alim Ozturk also contributing from the bench.
Parkinson added: “Josh is a very good player, he has come in and the lads in midfield have gone up a level.
“He has done really well and it just showed what he is all about; he is a very clever, intelligent player and did some good things.”