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 this afternoon.
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.
Hopes were high before kick-off as Pearson took Leicester back into the Championship at the first attempt and had the highest win ratio of any permanent manager at the club.
His side showed plenty of energy early on but they failed to fashion any meaningful opportunities.
And they were nearly caught out, with defender Sean St Ledger's last-gasp interception preventing Glenn Murray from converting Wilfried Zaha's cross.
The Foxes started to grow in stature after that, however, and Andy King's header was well saved by Julian Speroni, while the Palace goalkeeper magnificently clawed away a long-range effort from Gallacher that looked destined for the bottom right corner.
Beckford beat the offside trap to go clean through but his woeful first touch from goalkeeper Kasper Schmeichel's long punt cost the striker dearly.
The former Leeds frontman was culpable of spurning another opportunity when he could not direct his free header on target and it remained all square at the interval.
Palace came firing out of the traps at the beginning of the second half so it came as a surprise when the hosts broke the deadlock in the 55th minute.
Richie Wellens collected the ball from Paul Konchesky before playing through Beckford and he put his first-half woes behind him to slot home.
The striker had a chance to double his side's lead immediately after when he picked up a loose ball but after going clean through on goal, Beckford's tame effort was comfortably saved by Speroni.
His profligacy nearly came back to haunt Leicester but Kagisho Dikgacoi blazed over from close range, while debutant Chris Martin - on-loan from Norwich - had a bullet header saved by Schmeichel mere minutes after coming on.
The Foxes weathered the storm and Gallacher and Wellens both forced Speroni into action before the former doubled his side's lead in the 71st minute.
There looked to be little danger when he picked up the ball 25 yards from goal but after being given room to manoeuvre, the winger curled delightfully into the top-right corner.
High on confidence, Gallacher settled matters three minutes later with another exquisite strike, this time his first-time blast from long range rocketed past a despairing Speroni.