Danny Kerry's side took the lead in the sixth minute when Cullen lashed one of her trademark penalty corners past Yimeng Zhang but the Beijing silver medallists, beaten 3-0 by world champions Argentina yesterday, continued to make life tough.
However, a string of unconverted chances, Alex Danson and Helen Richardson went particularly close, didn't help the hosts' cause.
And it wasn't until two minutes from time that Susie Gilbert showed her predatory instincts, pouncing on Richardson's rebounded shot to double the advantage.
The pressure finally off, Cullen then gave the scoreline a comfortable feel with her second penalty corner but Kerry still demanded improvements.
"I am still frustrated that we went into the break only one goal up after the number of chances we had but I am really pleased with the goals we did score, especially the second one because we have been doing a lot of work on that in training," he said.
“We had a very quick debrief following yesterday’s game. We knew exactly what we needed to do and I think we did it."
Great Britain will have a day of rest on Friday before playing Argentina, considered their biggest rivals for Olympic gold this summer. They are also likely to play the world champions again in Sunday's final, with wins over Korea and China securing Kerry's team their place in that match whatever the result.