Putting S.O.S. Fundamentals
Solid - hit the putt solid
Online - start the putt on the target line
Speed - hit the putt the correct speed

Every stroke has a flaw

When the heat is on, every player's stroke shows their flaw - you've seen it ... and probably felt it :(

The tendency might be to increase grip pressure which causes the stroke to go outside the intended line.
They can hang on and try to steer the putt, and push it at impact.
There are all sorts of things that happen when nerves kick in ... let's change the subject.

The Tour players and coaches I'm around know the flaw, and train to eliminate it. It is a 2 step process:
1. Learn the tendency under pressure
2. Train to minimize the tendency

1. Learn your tendency. Set up a rectangle of tees.
Make strokes and hit putts, noting which tees you hit most often. That is your tendency.

2. Train against that tendency.
For instance: If you tend to move the putter outside the line - either in the backswing or follow through - train using the toe of the putter for negative reinforcement. If you come inside, use the heel. 

First, let your putter ride the rail. Then put the rail 1/2" away from your putter and make a stroke. Make strokes NOT hitting the rail.

It's time to get "pressure-proofed."