Before the Dell Accenture Match Play, Poulter was informed that a quarter-final spot would be enough to earn a place at Augusta, only to be told 10 minutes before his last-eight tie that he would narrowly miss out unless he reached the last four.
Poulter subsequently lost to Kevin Kisner and was in two minds about competing at the Houston Open, but the Englishman produced one of the most remarkable performances in PGA Tour history, coming from 123rd place after the first round to win a playoff against Beau Hossler on Sunday.
The new world number 29 has acknowledged that his triumph is "amazing", and that he had been left exhausted by the contrasting emotions that he has experienced over the past 10 days.
After his victory, Poulter told Sky Sports News: "I wanted to win this week. Last week was a big disappointment, as well as I played and not quite getting it done.
"I came here with a mindset of being super-aggressive - I was probably a bit too aggressive, a bit angry on Thursday - but I settled back down Friday, Saturday, Sunday and it truly is amazing to get this done today.
"I'm drained. Last week was emotional but I'm going to find the energy for next week. To be back in the top 50 nicely, to have a two-year exemption, to be going there freewheeling is going to be really nice."
Poulter last appeared at The Masters in 2015, where he claimed a sixth-place finish.