The large open-circuit voltage deficit (V-oc,V-def) is the key issue that limits kesterite (Cu2ZnSn(S,Se)(4), [CZTSSe]) solar cell performance. Substitution of Cu+ by larger ionic Ag+ ((Ag,Cu)(2)ZnSn(S,Se)(4), [ACZTSSe]) is one strategy to reduce Cu-Zn disorder and improve kesterite V-oc. However, the so far reported ACZTSSe solar cell has not demonstrated lower V-oc,V-def than the world record device, indicating that some intrinsic defect properties cannot be mitigated using current approaches. Here, incorporation of Ag into kesterite through a dimethyl sulfoxide (DMSO) solution that can facilitate direct phase transformation grain growth and produce a uniform and less defective kesterite absorber is reported. The same coordination chemistry of Ag+ and Cu+ in the DMSO solution results in the same reaction path of ACZTSSe to CZTSSe, resulting in significant suppression of Cu-Zn defects, its defect cluster [2Cu(Zn) + Sn-Zn], and deep level defect Cu-Sn. A champion device with an efficiency of 12.5% (active area efficiency 13.5% without antireflection coating) and a record low V-oc,V-def (64.2% Shockley-Queisser limit) is achieved from ACZTSSe with 5% Ag content.