Ritchie Humphreys had extracted a diving save from David Martin inside the first minute with a well struck shot from 25 yards, but City produced the perfect riposte with a goal after three minutes.
The ball squirmed free in the Pools area following Lloyd Dyer's cross, and the Foxes skipper reacted quickly to ram the ball home from two yards.
Oakley was then City's hero at the other end on 24 minutes when he cleared Michael Nelson's drive off the line before James Brown dragged a shot wide of the far post.
Matty Fryatt could have given Leicester a two goal lead just before the break but instead of bulging the net from close range he scooped Steve Howard's flick-on over the bar.
City continued to waste chances and almost paid for their profligacy five minutes from the end when they had to rely on Martin's sprawling save to keep out Brown's 16-yard drive with Nelson heading the resultant corner narrowly over.