The save can be achieved when the tying run is on deck-so you could be winning by one run or by five runs depending on the situation.
There is also a rule that says a relief pitcher will get a save if he pitches three innings, ends the game, and is not the winning pitcher, regardless of score. Because of this rule, in the most lopsided victory in major league history*, reliever Wes Littleton was credited with saving a 27-run lead because he pitched three innings.
* Box here: http://www.Baseball-reference.com/boxes/BAL/BAL200708221.shtml
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