City took the lead in the third minute when, after Oakley and Richie Humphreys had challenged for a Lloyd Dyer cross, the ball squirmed free for the City skipper to ram home from two yards.
It was the perfect riposte to Hartlepool, who had given the Foxes a scare inside 60 seconds when Humphreys' well-struck shot from 22 yards had extracted a diving save from David Martin.
After Leicester's goal, Dyer produced two good crosses in quick succession for Matty Fryatt, who drove the first just wide and then saw the second smothered by the keeper.
Oakley was then City's hero at the other end when on 24 minutes he cleared Michael Nelson's drive off the line before James Brown dragged a shot wide of the far post.
Fryatt could have given Leicester a two-goal cushion just before the break but instead of finding the net from close range he scooped Steve Howard's flick over the bar.
Howard had a 55th minute chance to score against the club he began his career with but his shot from Andy King's cross was blocked by Aaran Lee-Barrett.
On the hour-mark, Nicky Adams provided Howard with another glimpse of goal but the big striker's drive was again kept out by the busy Hartlepool keeper.
Hesitancy between Nelson and his keeper was seized upon by Fryatt, whose tight-angled shot drifted just wide.
City continued to push but they were foiled by Lee-Barrett again on 80 minutes when he got down well to Fryatt's drive from another Howard knock on.
The Foxes almost paid for their profligacy five minutes from the end when they had to rely on a sprawling save by Martin to keep out Brown's 16-yard low drive with Nelson heading Jamie McCunnie's resultant corner just over.