The win marked a milestone for the world No. 3 as it was his first on the regular European Tour.
Johnson began the day in a tie for first with a resurgent Li, and the pair were nip-and-tuck trading a birdie each on the front nine.
Li then recovered beautifully from a poor tee shot on the ninth, holing a chip approach from above the green to take the a 1-shot lead.
Lewis dragged himself into contention with a stunning opening run of five birdies, and he moved to within a shot of the leaders as both bogeyed the 10th, but Johnson reacted well and retook the lead form Li with a superb tee shot at the 11th and a fine left-to-right putt at the 12th for back-to-back birdies.
Li then struggled to maintain his form and followed up a disappointing bogey at the 13th with another at the 14th after going into the bunker above the green on his approach.
Li put a little late pressure on Johnson with an approach to two feet for birdie at the 15th and the American briefly wobbled as he found the water on the 16th before scrambling for bogey.
But Johnson was peerless at the death, hitting a fine long putt from off the green at the 17th to set up a birdie and a huge drive at the 18th to gain another shot and win by 2 strokes.
Li took second place outright by holing a five-foot birdie at the 18th to finish at 17 under, 1 shot clear of Lewis. Min Woo Lee finished in fourth at 15 under with an excellent final-round 63, and France’s Alexander Levy finished fifth at 14 under.