We present a measurement of the a production cross section sigma((u) over bar) in p (p) over bar collisions at root s = 1.96 TeV using 5.4 fb(-1) of integrated luminosity collected with the D0 detector. We consider final states with at least two jets and two leptons (ee, e mu, mu mu), and events with one jet for the e mu final state as well. The measured cross section is sigma((u) over bar) = 7.36(-0.79)(+0.90)(stat + syst) pb. This result combined with the cross section measurement in the lepton + jets final state yields sigma((u) over bar) = 7.56(-0.56)(+0.63)(stat + syst) pb, which agrees with the standard model expectation. The relative precision of 8% of this measurement is comparable to the precision of the latest theoretical calculations.