Bellingham's thumping header from a deflected Bukayo Saka cross proved to be the difference between the two sides, with Gareth Southgate's side taking an early lead in Group C.
Serbia put in a much-improved second-half performance after struggling in the opening 45 minutes, but Dragan Stojkovic's side found it difficult to carve out clear chances and were ultimately beaten in Gelsenkirchen.
England sit at the top of Group C on three points, with Slovenia and Denmark playing out a 1-1 draw in the section's opening fixture earlier in the evening.
Bellingham header wins it for England
There were plenty of familiar names in the Serbia XI, with Dusan Vlahovic and Aleksandar Mitrovic operating in the final third of the field, while Sergej Milinkovic-Savic, Filip Kostic and Nemanja Gudelj were notable inclusions in the side, but captain Dusan Tadic was only on the bench.
As for England, Trent Alexander-Arnold, as expected, was given the nod in midfield alongside Declan Rice and Bellingham, while Marc Guehi and Kieran Trippier both started at the back.
It did not take long for England to take control of the possession, with Serbia sitting deep and then looking to hit long balls towards Vlahovic and Mitrovic.
The onus was on the Three Lions to make things happen, and the likes of Bellingham and Phil Foden were seeing plenty of the ball, but the Serbian team were unmoved in the opening 10 minutes.
England managed to make the breakthrough in the 13th minute, though, with Bellingham thumping a header into the back of the net after Saka's cross was deflected into a dangerous area.
Serbia had a chance to level the scores in the 20th minute of the match, with Mitrovic finding space outside the box after some lacklustre defending from Alexander-Arnold, but the striker's effort whistled just wide.
Down the other end, Kyle Walker broke into the box after smart work from Alexander-Arnold, but there were no takers on the Manchester City defender's low cross into a dangerous area.
It was a similar story in the 37th minute, with Saka breaking into the box before delivering, but it went to a red shirt, with the opportunity coming after a strong spell from Serbia.
Bellingham's goal was the difference at the half-time break, but England did not have it all their own way, with Serbia showing enough to suggest that they could fight back in the second period.
Serbia will feel that they deserved a point
Serbia made a positive start to the second half, with the Eagles more aggressive with their work, and England were far from comfortable despite having the lead.
Filip Mladenovic came close to meeting a low cross from Vlahovic in the 52nd minute after smart work from the Juventus striker, before Alexander-Arnold tested Predrag Rajkovic with a strike down the other end.
Serbia had a shout for a penalty just before the hour as Mitrovic went down inside the box under contact from Trippier, but the referee was not interested, and the ex-Fulham striker was substituted soon after.
Kane came close to doubling England's lead in the 77th minute with a thumping header from a Jarrod Bowen cross, but his effort was pushed against the crossbar by Serbia's goalkeeper.
Down the other end, England goalkeeper Jordan Pickford was at full strength to keep out a powerful strike from Vlahovic, before Kane headed one off the line from the resulting corner.
It was far from convincing from the Three Lions, but they managed to get the job done against a stern Serbia outfit to start their tournament with a vital three points.
When are Serbia, England next in action?
England will be bidding to make it two wins from two fixtures in the section when they take on Denmark on Thursday, while Serbia will tackle Slovenia on the same day.