Wood netted a first-half treble against a side looking on course for relegation and Matty James completed an emphatic victory with a well struck shot on 52 minutes.
The result moves Leicester into third, level on points with Crystal Palace and Middlesbrough, while the Robins are still rock-bottom.
Wood only joined the Foxes at the start of the month from West Brom after a successful loan spell at Millwall and manager Pearson acknowledged the difference has made in such a short space of time.
Pearson said: "Chris Wood has taken his chances for us and scored some early goals, which makes a big difference.
"He is a very focused young player who has fitted in straight away and gives us a height and physical presence up front, which perhaps we lacked.
"It is not easy to sign quality players in January and I am delighted to have secured him early in the window.
"We created a lot of chances to today and I am also very pleased to have kept a clean sheet.
"We could have passed the ball better at times and the second half seemed to go on forever. But we protected our lead and managed to build on it."