The 2001 US PGA Championship winner carded a final round of 70, level par, which included a crucial birdie on the 16th hole to deny Jiménez a chance of a second Senior Major title.
The 51 year old started the day one stroke behind 54-hole leader Kelly, who carded a final round of 72, two over par to drop to a share of second.
After starting the day three under par through seven holes, Jiménez made the turn level par after a double bogey-bogey finish to his front nine. Another bogey followed on the 12th hole, but he finished strongly with birdies on the 15th and 18th holes to take the clubhouse lead on two under par.
Toms, playing in the final pair with Kelly, found a fairway bunker on the par four 17th, but made a superb 20-foot putt to save par and remain on three under. He then parred the final hole to secure his first win on the over-50s circuit.
"Today was a really tough day," said Toms. "The wind made it very difficult for us to pull a club. I kept hitting it over the greens and having to get up-and-down. I never felt like I was in total control. Even from the fairway, I wasn't able to get the ball close to the pin.
"I was getting frustrated with that, but at the same time my short game felt good and I just hung in there. I wanted to be there at the end to have a chance."
Jiménez, who won his maiden Senior Major Championship at the Regions Tradition earlier this season, said: "I have to congratulate David because in golf you have 14 clubs in the bag, you have to be yourself and you have to be focused. He's the one who did it better than anyone. My game was not the way it should be."
Paul Broadhurst, winner of the KitchenAid Senior PGA Championship in May, finished in a share of fifth place on one under par.
"I played pretty well in practice, then I lost my driver on Friday afternoon. That was a bit of a concern. I went and hit balls afterwards and sorted it out a little bit, so I'm pleased that I managed to work it out myself.
"I was pleased with a good weekend, shooting under par both days. I'll take a lot from this week."
Staysure Tour members Bernhard Langer and Vijay Singh finished tied 16th, South Africa's David Frost shared 24th place, Philip Golding finished tied 28th and Chris Williams shared 31st place.