How have you seen warior characters in fantasy books overcome spellcasters?
Usually by being faster than they are, and getting off an arrow or sword blow before the wizard can do much of anything. Or they have a McGuffin that lets them escape the brunt of the wizard's power in time to finish him off.
'Need' is a good example of that in the Tarma and Kethry books. It's a minor artifact that makes a warrior almost invulnerable to magic (and conversely makes a wizard the equal of a superb warrior), as long as the warrior is working towards that sword's special purpose ('Protect all women').
So, in that case, spellcasting probably took more than the typical "Standard Action" and the wizard had *very* low Hit Points and no protective magic in place (even though he was anticipating the encounter).
Most magic in fantasy books is not the all-combat-oriented magic you see in D&D. I've seen very, very few mages in books with any sort of shielding spell against physical attacks except items they've created. The ones that do (Harry Dresden's shielding charm comes to mind) have limited charges or effects. They'll provide perfect protection from 1, 2 maybe 3 attacks and then it goes down.
Spellcasting in classic fantasy is almost never quick stuff useful in combat. In modern fantasy, you'll see it a lot but it's usually inversely proportional - quick spells do little damage or they are over soon as well. Usually there will be dire 'in game' penalties for using magic to kill, so a lot of magic stuns, blinds or paralyzes people.
There are some times that mages tap into hidden forces or deep emotions to do large, quick, devastating combat magic. In those cases, warriors run or they die, no question about it. Typically this is not something someone can just do off the cuff, though, and comes at major climaxes. And a lot of times the mage in question pays for it by either being powerless for a time thereafter or other side effects.
Characters in books never have the huge buckets of hit points they do in D&D, so a fist to the jaw or a dagger in the back is enough to put down or kill pretty much any normal person. Think if you had the hit points you had in AD&D (fighter, maybe 12; mage, 3-4) and then it never, ever got any better. You'd be closer to the way most books work. People live through fights by having good armor, avoiding blows, or by never letting a fight occur in the first place.
Another 'balancing' thing you'll see now and again is 'all spells are not created equal'. In D&D, every spell is just as easy to learn as any other. In most books, that's just not the case. In a series I just finished 'A Young Man Without Magic' by Lawrence Watt-Evans, glamor and illusion magic is very rare because it requires a very powerful sorcerer to create them. Any hedge witch can do a little healing and some simple beguilement, but a major gut wound is beyond them. Similarly, in most books the death-dealing combat spells are usually rare; hard to find and/or hard to learn.