ESP8266 cannot read DHT22

I am trying to build a WiFi humidity and temperature sensor. My board is a nodeMCU using the ESP8266 connected via USB. The board is working fine with various WiFi examples and various serial examples. Hence I guest my environment is OK.

Now I am trying to connect a DHT22 to read temperature and humidity. To reduce the error sources I boiled down my code to the standard DHT example:

// Example testing sketch for various DHT humidity/temperature sensors
// Written by ladyada, public domain
#include "DHT.h"
#define DHTPIN 2
#define DHTTYPE DHT22   // DHT 22  (AM2302)
DHT dht(DHTPIN, DHTTYPE);

void setup() {
  Serial.begin(9600);
  Serial.println("DHTxx test!");
  dht.begin();
}

void loop() {
  delay(2000);

  float h = dht.readHumidity();
  float t = dht.readTemperature();
  float f = dht.readTemperature(true);
  if (isnan(h) || isnan(t) || isnan(f)) {
    Serial.println("Failed to read from DHT sensor!");
    return;
  }

  Serial.print("Humidity: ");
  Serial.print(h);
  Serial.print(" %\t");
  Serial.print("Temperature: ");
  Serial.print(t);
  Serial.println(" *C ");
}

Nevertheless I always get the message "Failed to read from DHT sensor!".

Regarding the hardware I tried connecting the sensor with or without the 10k resistor, tried different DHTs and different pins. To rule out the DHTs I connected them with an Arduino Nano where these are working fine (both with and without resistor and using the same code). The only difference I see is that the Arduino is using 5V while the ESP8266 is using 3.3V - which is nonetheless inside the rating of the DHT.

Any ideas?