SOURCE

var app = new Vue({
    el: '#app',
    data() {
        return {
            dialogVisible: false,
            mousedownCls: [],
            mouseupCls: []
        }
    },
    methods: {
        dialogMousedown(e) {
            this.mousedownCls = [...e.target.classList]
        },
        dialogMouseup(e) {
            this.mouseupCls = [...e.target.classList]
        },
        beforeDialogClose(done) {
            const isWrapper = this.mousedownCls.includes('el-dialog__wrapper') && this.mouseupCls.includes('el-dialog__wrapper')
            const isClose = this.mousedownCls.includes('el-dialog__close') && this.mouseupCls.includes('el-dialog__close')
            if (isWrapper || isClose) {
                done()
            }
        }
    }
});

<div id="app">
	<el-button type="text"
      @click="dialogVisible = true">
      点击打开 Dialog
    </el-button>
    <el-dialog title="提示"
      :visible.sync="dialogVisible"
      :before-close="beforeDialogClose"
      @mousedown.native="dialogMousedown"
      @mouseup.native="dialogMouseup">
      <span>这是一段信息</span>
      <div slot="footer"
        class="dialog-footer">
        <el-button @click="dialogVisible = false">取 消</el-button>
        <el-button type="primary"
          @click="dialogVisible = false">确 定</el-button>
      </div>
    </el-dialog>
</div>