Cheered on by a gallery that was several thousand strong, the 41-year-old Englishman shot rounds of 70 and 68 to book one of only three spots available at the Birkdale showpiece from final qualifying at the Bedfordshire course.
Poulter had his best major at Royal Birkdale in 2008 when he was runner-up to Padraig Harrington. However, Padraig Harrington eagled the par-5 17 hole and ran out a four shot victor to successfully defend the championship he won 12 months previously.
The Open Championship is July 20-23.
After going to the turn in level par in the afternoon round, he then birdied his 11th and 15th holes to keep his hopes alive.
"I played awesome, especially to be bogey-free this afternoon", he said after making a quick phone call to his father and coach, Drumoig Golf Centre PGA professional Stuart, to tell him the good news. "This is my first time playing links golf and I feel as though I handled it well in typical summer Scottish conditions".
Poulter is never short of confidence and feels he can compete at Royal Birkdale. It's going to be a busy run.
A crowd of about 250 locals and members turned up to watch Poulter play in the company of English amateur Jack Singh Brar and Jeev Milkha Singh of India, who withdrew after shooting 75 in the morning.
Kapur was thus among the three players with the best scores who qualified from The Marquess' Course at Woburn.
Meanwhile, if you need to know how to successfully navigate Final Qualifying for The Open, we suggest you turn to Matthew Southgate.
Former Purdue player Kapur made a 4,167-mile round trip from his home in New Delhi to tee it up at Woburn. Playing most of his golf on the Asian Tour, the one-time college golfer at Purdue flew more than 2,000 miles exclusively for the qualifier and the chance to get into his third Open.