World number two Bingham started the match in style with a superb break of 127 before a run of 67 helped him open up a two-frame lead.
Gloucester's Milkins, who was appearing in his sixth ranking semi-final and bidding to reach his maiden final, made a break of 55 in the third frame but Bingham snatched it on the black to land a decisive blow.
The 40-year-old from Basildon then surged to victory with successive breaks of 71, 61 and then 101 - and he'll now be aiming to win his first ranking title since lifting the World Championship trophy back in 2015.
Sunday's final will be first to nine frames, with the winner lifting the Ray Reardon Trophy and taking home a top prize of £70,000.
Earlier, Judd Trump defeated Scott Donaldson 6-3 to book his place in the final as he targets a seventh ranking title of his career.
The Bristol cueman, who came through a thrilling quarter-final with Barry Hawkins a day earlier, got off to a great start as breaks of 131, 55 and 65 across the opening five frames saw him surge into a 4-1 lead.
Donaldson took the next two, with the help of a break of 74 in the seventh, to cut the deficit but Trump wrapped up the victory with back-to-back runs of 82 and 60.
The world number four is hunting for his first Welsh Open crown and second ranking title of the season having won the European Masters in October.
After reaching his 13th ranking final, Trump told worldsnooker.com: "It was a bit of a struggle today. I was good at the start and at the end, in the middle I let it slip a little bit, but I managed to hold on and win.
"Scott started to enjoy himself when he came back to 4-3. At the start he was a bit nervous so it was important for me to get a good lead. The crowd started to get behind him, they want to see a close game. It was important for me to be professional and not miss anything easy.
"I had some tremendous support, the crowds all week have been as good as anywhere. Today it was packed out, it had an extra buzz, especially because it is a semi-final."
Welsh Open final: Session times & odds
Sunday February 19
Afternoon Session (1300 GMT)
Final (Best of 17 frames)
TV Coverage: Eurosport 2
Judd Trump v Stuart Bingham
Evening Session (1900 GMT)
Final (Best of 17 frames)
TV Coverage: Eurosport 2
Judd Trump v Stuart Bingham
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