Only if your opponent is evenly matched with you. Generally knife fights are like sword fights, being more skilled usually means a very short fight.

In fencing, there is an odd thing called "right of way". It works like this, a touch is only valid if you presented your intent to attack and thus gained right of way. It is a very subtle thing, but it has a very important implications for the sport.

It exists because the first person to score a touch gets the point. If right-of-way didn't exist then the right thing to do when your opponent goes for your head would be to poke him very quickly on the arm or torso and just take the blow to the head. If you hit him first, it would be your point. This is pretty silly though and would be an artifact of the stylization of fencing. No rational person would opt to get a small cut on the opponents arm or chest in exchange for a large gash on their head.

In a bloody duel, 90% of your energy needs to be focused on not getting hit. It would be a hollow victory if you got yourself just as cut up as your opponent.

This was always a problem when fencing with new fencers. They didn't understand the right of way and didn't know how to read your actions, so it was very easy to go for a blow and get slapped on the side for it. I'd get the point for having right of way, and I'd have to explain what a silly move it was. Yes, they hit me first, but they still got hit.

It's even harder to parry a knife than a sword. Be ready to bleed.

I've never fenced, but have done extensive knife fighting training both specifically and as part of jujitsu training. I've practiced a ton with rubber chalked knives, both armed and disarmed against an armed opponent.

Untrained fighters are, in my experience, usually pretty easy to either disarm or to block their knife hand/arm with my non-knife hand. If they are VERY quick, I might take a minor slice on my hand or forearm, but I've never sparred against a non-specially trained opponent who's been able to either "kill" me, or prolong the fight more than a few seconds.

Thankfully I have never been in a real knife to knife fight, so YMMV.

Swords are much longer (unless you really liked Crocodile Dundee) - that means you're more likely to successfully parry or block if you're skilled. But a knife? Avoiding it and getting cut are the only options really.

No matter who is better skilled if you go into any knife fight, where you or your attacker has a knife and you are not prepared to bleed you are wrong.