Pearson left Hull earlier this week to retake the reins at the King Power Stadium and replace Sven-Goran Eriksson - less than 18 months after he walked away to manage the Tigers.
The Foxes enjoyed immense success under Pearson first time around and Jermaine Beckford's opener set them on their way to a resounding victory. After a goalless first half in which the striker spurned the best opportunities, Beckford opened the scoring with a cool finish.
Gallacher's two long-range strikes settled matters and ensured a happy homecoming for Pearson.
Leicester move level on points with Palace, who have now not scored in the npower Championship in their last four matches, to put themselves firmly back in the play-off hunt.
Meanwhile, Nicky Maynard underlined his importance to Bristol City's revival with the goals which sunk Millwall 2-1.
Striker Maynard, who was a target for West Ham and Leicester in the summer, is out of contract at the end of the season and will be sold in January unless he agrees a new one.
But new City boss Derek McInnes is desperate to keep hold of the 24-year-old, and he showed just why with a well-taken double.
Maynard opened the scoring in the 15th minute and struck the winner in the second half after Jay Simpson had briefly hauled Millwall level.
It means City have now picked up 10 points from five matches since McInnes took over, compared to a measly six from their previous 11 outings.