Dutch rivals AZ Alkmaar were also among the goals, routing Swiss side Grasshoppers 5-2 to make it two wins from two, a record matched by Tottenham Hotspur, Newcastle United, Blackburn Rovers, Rangers, Panathinaikos and Belgium's Zulte-Waregem.
Elsewhere, Livorno goalkeeper Marco Amelia scored with an 88th-minute close-range header to rescue a draw for the Serie A side in a 1-1 draw at Partizan Belgrade.
Ajax appear to have shrugged off the disappointment of failing to reach the group stage of the Champions League, visitors Austria Vienna no match for the Dutch league leaders.
Huntelaar broke the deadlock from close range 10 minutes before halftime after goalkeeper Szabolcs Safar had blocked a Zdenek Grygera header. Ajax sealed the points with two goals in four minutes midway through the second half, Edgar Manucharyan scoring with a deflected strike and Huntelaar nodding in a free kick.
The four British sides in action all enjoyed victories.
Bulgaria forward Dimitar Berbatov was instrumental in firing Spurs to the brink of qualification to the knockout stages, scoring twice and making another as Martin Jol's side overcame Club Bruges 3-1 in Group B at a sold-out White Hart Lane.
Spurs did fall behind when Ibrahim Salou curled a fine effort to hand Bruges a 15th-minute lead but his finish was emulated by Berbatov less than three minutes later, the Bulgarian netting with an exquisite volley.
Berbatov's perfect volleyed pass set up a second for Robbie Keane midway through the second half and he then headed home a cross from Hossam Ghaly.
Spanish misfit Albert Luque hit the only goal for Newcastle United who pulled off a 1-0 win in Group H away to Serie A high-flyers
Luque, who has made just a handful of appearances since a big-money move from Deportivo Coruna in Aug. 2005, headed home James Milner's cross eight minutes before halftime.
TEMPERS FLARED
Palermo, starting with just three of the side who began their 3-2 win against Fiorentina at the weekend, were kept out by Newcastle's teenage goalkeeper Tim Krul, making his debut.
Blackburn scored three goals in the final 15 minutes to rout Basel 3-0 in Group E while a 2-0 home win over Maccabi Haifa put Rangers top of Group A.
A late penalty from Claudiu Niculescu gave Dinamo Bucharest a winning start in Group B, his spot-kick securing a 2-1 home win over Besiktas as tempers flared in the Romanian capital.
Dinamo, in spectacular form domestically with 13 league wins from 13, led through Adrian Cristea only to be pegged back by Brazilian Deivson. Besiktas's Gokhan Zan was sent off along with Dinamo's Cosmin Moti just before Niculescu's penalty and the hosts finished with nine men after midfielder Andrei Margaritescu was sent off deep into stoppage time.
AZ Alkmaar made it two wins from two in Group C, coming from a goal down to rout Swiss league leaders Grasshoppers 5-2 away from home.
Democratic Republic of Congo midfielder Mbula Mbata put Grasshoppers ahead but the Dutch side, semi-finalists in 2005, hit back with two goals in the five minutes early in the second half through Shota Arveladze and Demy de Zeeuw. Eduardo made it 2-2 on 62 but AZ then hit top gear, Mouassa Dembele netting twice with Maarten Martens adding the fifth.
The top three teams in each of the eight groups qualify for the knockout phase where they are joined by the eight Champions League third place finishers.
