"He was a good friend to us all and it was great to get the job done for him today," Van Pelt said.
The 55-year-old Steele, who was caddying for Kirk Triplett, collapsed in a golf club car park in North Carolina a week ago.
Van Pelt, the world number 24, had rounds of 70 67 67 and 68 to finish 16 under par on 272 and pocket a cheque for $333,330.
"I've had a lot of top 10s this year and it's great to get a win," said Van Pelt after starting the day one shot clear of world number 10 Jason Dufner, who closed with a 69 to finish second.
Dufner paid tribute to his fellow American, saying: "Bo played really good today, put a lot of pressure on me to make something happen but I couldn't quite do it. You're going to have a hard chance winning when someone plays as well as Bo did."
Spaniard Alejandro Canizares shot 68 on the final day to grab outright third at 11 under par. Argentina's Emiliano Grillo, who led for much of the tournament, closed with a 74 to finish in a tie for fifth.
By the 10th hole it became clear that the final day had become a shoot-out between good friends Van Pelt and Dufner.
Van Pelt opened up a three-shot lead by the 14th tee but there was a two-shot swing when Dufner almost holed his second at the short par four and tapped in for birdie, while his rival took a bogey.
Dufner, however, found a greenside bunker at the next hole and Van Pelt made a regulation birdie to stretch the margin to two.
When Dufner's short par putt lipped out at 16, Van Pelt made par and the gap was back out to three. Van Pelt gave a shot back at the par-three 17th but still looked comfortable on the last tee.
The 37-year-old Van Pelt collected his third career victory and will now defend the title he won in Malaysia in 2011 - the Pacific Asia Classic.
- Jason Dufner