We show that combining a direct measurement of the Higgs total width from the H \to ZZ \to 4l lineshape with Higgs signal rate measurements allows Higgs couplings to be extracted in a model-independent way from CERN Large Hadron Collider (LHC) data. Using existing experimental studies with 30 fb-1 at one detector of the 14 TeV LHC, we show that the couplings-squared of a 190 GeV Higgs to WW, ZZ, and gg can be extracted with statistical precisions of about 10%, and a 95% confidence level upper limit on an unobserved component of the Higgs decay width of about 22% of the SM Higgs width can be set. The method can also be applied for heavier Higgs masses.