diff --git a/conn.go b/conn.go
index d73aa9258..42e6718ec 100644
--- a/conn.go
+++ b/conn.go
@@ -91,6 +91,7 @@ type Conn struct {
 	reading               chan struct{}
 	handshakeRecv         chan recvHandshakeState
 	inboundPacketInject   chan addrPkt
+	pendingRead           chan readResult // in-flight nextConn read, owned by the read loop
 	cancelHandshaker      func()
 	cancelHandshakeReader func()
 
@@ -964,12 +965,33 @@ func (c *Conn) InjectInboundPacket(p []byte, rAddr net.Addr) {
 	c.inboundPacketInject <- addrPkt{rAddr, p}
 }
 
+type readResult struct {
+	data  []byte
+	rAddr net.Addr
+	err   error
+}
+
 func (c *Conn) nextPacket(ctx context.Context) ([]byte, net.Addr, error) {
-	type readResult struct {
-		data  []byte
-		rAddr net.Addr
-		err   error
+	// An injected packet can win the select below. Keep the network read in
+	// flight for the next call instead of abandoning it, or whatever it reads
+	// next is dropped.
+	if c.pendingRead == nil {
+		c.pendingRead = c.startRead(ctx)
 	}
+
+	select {
+	case p := <-c.inboundPacketInject:
+		return p.data, p.rAddr, nil
+	case p := <-c.pendingRead:
+		c.pendingRead = nil
+
+		return p.data, p.rAddr, p.err
+	case <-ctx.Done():
+		return nil, nil, ctx.Err()
+	}
+}
+
+func (c *Conn) startRead(ctx context.Context) chan readResult {
 	readCh := make(chan readResult, 1)
 
 	go func() {
@@ -998,14 +1020,8 @@ func (c *Conn) nextPacket(ctx context.Context) ([]byte, net.Addr, error) {
 			rAddr: rAddr,
 		}
 	}()
-	select {
-	case p := <-c.inboundPacketInject:
-		return p.data, p.rAddr, nil
-	case p := <-readCh:
-		return p.data, p.rAddr, p.err
-	case <-ctx.Done():
-		return nil, nil, ctx.Err()
-	}
+
+	return readCh
 }
 
 func (c *Conn) readAndBuffer(ctx context.Context) error { //nolint:cyclop