A player who doesn't [buckle under][1] pressure, could be said to [deliver the goods][2]. And I would also describe such a player as being *ruthless* and *consistent*.

However, a slang term which fits the Op's request is **clutch**:  
[to perform under pressure][5]
*In the last few seconds of a close game, only a player with clutch can lead the team to victory. (Derived from the clutch mechanism in a manual car, where perfect timing can mean the difference between a launch and a stall)*


A reputable baseball coach has this to say: <sup>[1][4]</sup>

>  If a hitter is averaging .333 and gets a hit one time in three clutch
> situations, he is performing well **in the clutch**... normal performance
> under pressure is the goal, not super performance.
> 
> All too often an athlete gets the reputation as a "**great clutch
> player**" because of one or two performances that got a lot of media
> attention, but the truth of the matter is most of the time a "great
> clutch performer" is one who performs normally under pressure.

 



  [1]: http://idioms.thefreedictionary.com/buckle+under
  [2]: http://idioms.thefreedictionary.com/deliver+the+goods
  [3]: http://www.goal.com/en/news/1717/editorial/2013/02/06/3729809/why-mario-balotelli-has-never-missed-a-penalty-in-his-career
  [4]: http://www.hsbaseballweb.com/under_pressure.htm
  [5]: http://www.urbandictionary.com/define.php?term=clutch