'It feels unbelievable,' said Jacobsen. 'I've played in USGA championships since I was 15 years old. U.S. Juniors, U.S. Amateurs, U.S. Opens and now my first U.S. Senior Open I competed in. I won it. I'm speechless practically.'
Tom Kite, who held the lead on the back nine at Bellerive Country Club, fell apart with back-to-back bogeys from the 15th and a double bogey at the last to join Jay Haas in a tie for third at 10-under-par 274.
Jacobsen, a seven-time winner on the PGA Tour, made his Champions Tour debut in March but missed considerable time following hip surgery shortly thereafter. Now the 50-year-old is a major champion in only his third start on the elder circuit.
After heavy rains forced the postponement of the second round on Friday, play was backed up on the weekend, leading to a 36-hole finish on Sunday.
'I had a lot of adrenaline going today, so I think that helped me. I wasn't too excited about playing 36,' said Jacobsen. 'You have to think of it as a new day. If you think of it as a continuation, then pretty soon you start realizing you're playing 36, and you get tired.'
Jacobsen shared the lead with Kite after the second round, but fell two off the pace after Kite fired a 65 in the third round. That advantage soon faded, however, as Jacobsen birdied his first two holes of the final round to reach 11 under while Kite struggled with a bogey at the first.
Jacobsen stumbled to a bogey at the sixth but hit his second shot to 7 feet for a birdie at the seventh, and by that point he again found himself trailing Kite.
Kite, the 1992 U.S. Open winner at Pebble Beach, reached the green in two at the par-5 fourth and ran home the eagle putt to regain the top spot. He then dropped his approach inside 5 feet for a birdie at the fifth to pull two ahead at 14 under.
Kite kept on cruising and knocked his second shot within 8 feet of the hole for a birdie at the 11th. Kite then missed the green off the tee at the par-3 13th but was able to get up and down to save par.
The 54-year-old was not as fortunate at the 15th, however, as he bogeyed the hole after his tee shot found a bunker. Kite was in the sand again at the 16th and dropped another shot to fall back to minus-12.
Jacobsen was fighting to keep pace around the turn and drained a long birdie putt at the par-4 10th. He then made it two in a row with a birdie at the 11th.
After a bogey at the 12th, Jacobsen regained his composure and rolled in a 12-foot putt for a birdie at the 14th. He dropped another shot with a bogey at the 15th, but remained tied with Kite over the closing holes at 12 under.
At the par-4 18th, Kite scrambled away his chances and chipped his fourth shot from off the green to the front of the putting surface. Kite two-putted for a double bogey to complete a round of 72.
Jacobsen, needing only a par at the last, almost holed his birdie putt at the 18th. He followed with a tap-in par for the win.
Irwin, a two-time U.S. Senior Open winner, got to 10 under early on but fell off the pace with a bogey at the fifth and a double bogey at the par-3 sixth after his tee shot found the water.
He recovered with a birdie at the seventh and regained another shot with a birdie at the 10th. Irwin then played his second shot to 6 feet for a birdie at the 12th and tallied a birdie at the 17th to finish at 11-under-par 271.
'I'd love to go back and play three more, but unfortunately Peter played great. He's going to be a tremendous addition to the tour, and he brings a great personality, a great presence, and obviously great golf,' said Irwin. 'But I felt good today. I'm sure it'll set in tomorrow.'
Haas, who came close to earning his first Champions Tour title, almost holed out with his third shot at the last. Haas tapped in for par and a round of 68.
'I knew what I needed to do,' said Haas. 'I needed to make a two actually, but a three would have been helpful. I would have had a chance then. You know, I hit the shot in the air. It looked pretty good.'
Bob Gilder carded an even-par 71 to take sixth place alone at 9-under-par 275. D.A. Weibring was two shots further back at 7-under-par 277.
Fuzzy Zoeller, Craig Stadler, Walter Hall and Doug Tewell shared seventh place at 6-under-par 278. John Harris followed at 5-under-par 279.