Birmingham, who have failed to score at home in the league all season, put up a hugely spirited showing and went close to gaining an unexpected point despite losing Freda Ayisi to a red card before the interval.
It was the home side who made the brighter start but both Kerys Harrop and Jade Moore were unable to make the most of headed opportunities from Jo Potter’s free kicks inside the opening 10 minutes.
However, they suffered a major blow on moments before half time when striker Ayisi was sent off for a second yellow card within a couple of minutes.
Winger Ubogagu scored her fourth away goal for Arsenal when she calmly slotted home on 53 minutes after neatly exchanging passes with Natalia Pablos.
Skipper Karen Carney increasingly provided spirited Brum with their chief threat. Her dazzling right wing run and cross was bundled against a post by Remi Allen in the 65th minute before substitute Kirsty Linnett volleyed the rebound over.
The game’s late chances mostly went Arsenal’s way with Rebecca Spencer making a fine save to deny substitute Danielle Carter five minutes from the end.
“I was just pleased to get the opportunity to play 90 minutes,” said Ubogagu.
“It was a hard game against Birmingham but that didn’t surprise me too much. The standard of football in this division is very high and anyone can beat anyone else on their day.
“I’m new to the team and if I’m getting a star in our away games that’s great, but it was about winning the game tonight.
“We needed a good result after last week’s defeat by Liverpool and this leaves us well placed just a couple of points behind leaders Chelsea.”
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