Jacobson, whose bogey at 10 on Sunday was the only blemish on his scorecard all week, fired a four-under-par 66 that moved him to a 20-under total of 260, one shot ahead of Americans Ryan Moore and John Rollins.
"It feels unbelievable and it's a been a long time," said Jacobson. "I feel I've been getting closer and closer so it's really nice to pull this one off."
The 36-year-old Swede, who won three times on the European Tour in 2003 and nowhere since, started the day with a one-shot lead after firing a seven-under 63 on Saturday.
Moore stormed into contention with a blistering start that included five birdies on his first seven holes and he became Jacobson's biggest threat. The two were tied at 20-under for the tournament after the American carded consecutive birdies at the short par-four 15th and par-three 16th.
But Moore, playing one group ahead of Jacobson, missed a four-footer for par at the 18th while Jacobson was on the tee.
"That 18th hole is going to sting a little bit," said Moore. "Just put it in a bad place off the tee and maybe a little too aggressive with my second shot. Honestly, hit a pretty darn good bunker shot, almost made it. Hit my first bad putt of the day. It was just a pretty simple left center putt and I pushed it right."
Jacobson then got a huge break as his tee shot on the final hole appeared to be headed for a bunker but kicked off a bank and landed in the fairway. He landed his approach to about 13 feet and then two-putted for the win and $1.08 million.
His bid to become the first player since Lee Trevino in 1974 to play a bogey-free 72 holes and win on the PGA Tour ended when he failed to recover after sending his approach shot at the par-four 10th right of the green.
"I caught a mud ball there on the right side and hit a good strike and you just got to accept those, with a long iron it can take off sideways," said Jacobson, who got his first win in 187 PGA Tour starts. "So I got challenged but I dealt with it nicely and kept playing well."
Rollins, who started the final round four shots off the lead, returned a seven-under-par 63, including five birdies on the back nine.
"I played good all day and did all I could," said Rollins. "Today I stayed in the moment. I kept plugging along and stayed with what I was doing and managed to get in a good round."
American Michael Thompson finished alone in fourth after a blistering eight-under-par 62 that was the day's lowest round and included nine birdies over his final 15 holes.
Patrick Cantlay, who had a one-shot lead after the second round when the 19-year-old American became the first amateur to card a 60 on the PGA Tour, finished nine shots back of Jacobson following an even-par 70 in the closing round.
"I just learned what it's like to have a week on the PGA Tour, make the cut and compete with the guys," said Cantlay. "The fans here were great all week, very supportive and I thank them."
Scores on Sunday after the final round of the $6 million PGA Travelers Championship (USA unless noted; par 70):
260 - Fredrik Jacobson (SWE) 65-66-63-66
261 - John Rollins 65-68-65-63, Ryan Moore 64-70-64-63
262 - Michael Thompson 67-65-68-62
264 - James Driscoll 69-64-64-67
265 - Kevin Streelman 66-70-63-66, Andres Romero (ARG) 64-67-67-67, Bryce Molder 65-66-64-70
266 - Brian Davis (GBR) 65-67-68-66, Tom Gillis 66-69-66-65, John Merrick 67-66-66-67, Blake Adams 66-66-66-68
267 - Bo Van Pelt 66-65-69-67, Brendan Steele 68-64-67-68, Nick Watney 65-65-68-69, Webb Simpson 66-65-67-69
268 - David Toms 69-66-69-64, Chris Stroud 66-69-67-66, Heath Slocum 70-63-68-67, David Mathis 67-65-68-68, Tommy Gainey 66-69-65-68, Johnson Wagner 65-63-71-69, DJ Trahan 69-62-68-69
Notable others:
269 - Carl Pettersson (SWE) 68-68-65-68, Ian Poulter (GBR) 68-68-66-67, Aaron Baddeley (AUS) 67-67-66-69
270 - Jhonattan Vegas (VEN) 69-67-68-66, Martin Laird (GBR) 68-67-66-69, Alexandre Rocha (BRA) 65-66-69-70
271 - David Hearn (CAN) 66-67-70-68
272 - Vijay Singh (FIJ) 67-68-69-68
273 - Aron Price (AUS) 69-66-68-70
276 - Padraig Harrington (IRL) 69-67-71-69