diff --git a/src/net/fd_unix.go b/src/net/fd_unix.go
index 7ef10702ed..0f80bc79ac 100644
--- a/src/net/fd_unix.go
+++ b/src/net/fd_unix.go
@@ -201,6 +201,14 @@ func (fd *netFD) Read(p []byte) (n int, err error) {
 		return 0, err
 	}
 	defer fd.readUnlock()
+	if len(p) == 0 {
+		// If the caller wanted a zero byte read, return immediately
+		// without trying. (But after acquiring the readLock.) Otherwise
+		// syscall.Read returns 0, nil and eofError turns that into
+		// io.EOF.
+		// TODO(bradfitz): make it wait for readability? (Issue 15735)
+		return 0, nil
+	}
 	if err := fd.pd.prepareRead(); err != nil {
 		return 0, err
 	}
diff --git a/src/net/fd_windows.go b/src/net/fd_windows.go
index 49e79d6a95..b0b6769eb3 100644
--- a/src/net/fd_windows.go
+++ b/src/net/fd_windows.go
@@ -427,7 +427,9 @@ func (fd *netFD) Read(buf []byte) (int, error) {
 	if race.Enabled {
 		race.Acquire(unsafe.Pointer(&ioSync))
 	}
-	err = fd.eofError(n, err)
+	if len(buf) != 0 {
+		err = fd.eofError(n, err)
+	}
 	if _, ok := err.(syscall.Errno); ok {
 		err = os.NewSyscallError("wsarecv", err)
 	}
diff --git a/src/net/net_test.go b/src/net/net_test.go
index 94392928c2..b2f825daff 100644
--- a/src/net/net_test.go
+++ b/src/net/net_test.go
@@ -360,3 +360,57 @@ func TestAcceptIgnoreAbortedConnRequest(t *testing.T) {
 		t.Error(err)
 	}
 }
+
+func TestZeroByteRead(t *testing.T) {
+	for _, network := range []string{"tcp", "unix", "unixpacket"} {
+		if !testableNetwork(network) {
+			t.Logf("skipping %s test", network)
+			continue
+		}
+
+		ln, err := newLocalListener(network)
+		if err != nil {
+			t.Fatal(err)
+		}
+		connc := make(chan Conn, 1)
+		go func() {
+			defer ln.Close()
+			c, err := ln.Accept()
+			if err != nil {
+				t.Error(err)
+			}
+			connc <- c // might be nil
+		}()
+		c, err := Dial(network, ln.Addr().String())
+		if err != nil {
+			t.Fatal(err)
+		}
+		defer c.Close()
+		sc := <-connc
+		if sc == nil {
+			continue
+		}
+		defer sc.Close()
+
+		if runtime.GOOS == "windows" {
+			// A zero byte read on Windows caused a wait for readability first.
+			// Rather than change that behavior, satisfy it in this test.
+			// See Issue 15735.
+			go io.WriteString(sc, "a")
+		}
+
+		n, err := c.Read(nil)
+		if n != 0 || err != nil {
+			t.Errorf("%s: zero byte client read = %v, %v; want 0, nil", network, n, err)
+		}
+
+		if runtime.GOOS == "windows" {
+			// Same as comment above.
+			go io.WriteString(c, "a")
+		}
+		n, err = sc.Read(nil)
+		if n != 0 || err != nil {
+			t.Errorf("%s: zero byte server read = %v, %v; want 0, nil", network, n, err)
+		}
+	}
+}