Alastair Cook savoured a "very special" series win after England triumphed in India for the first time in almost 28 years.
India took just one wicket for the day, as debutant Joe Root continued his impressive start with an unbeaten 20 to help England finish 352-4 at stumps.
The result marks England's first victory in India in nearly three decades, and India's first home series loss in eight years.
Trott's wicket for 143, the only one to do so for the day, with Bell finishing on 116 not out and debutant Joe Root continuing his impressive start to finish on 20 not out.
After the result, the England captain paid tribute to the batting of Trott and Bell to see out the result.
"It's a very special day for us, it's been a special tour and we'll have great memories," he told Sky Sports afterwards.
"Today was a fantastic effort by Trotty and Belly. All right, it was a flat pitch, but how calmly they batted was fantastic.
"We were slightly surprised how low and slow the pitch was, and it got better as the game went on.
"We knew when we batted in the second innings we had to make it very hard to take those wickets so credit to our batsmen for fronting up and taking on that challenge."
The series success was all the more impressive after a heavy nine-wicket defeat in the first Test in Ahmedabad, which prompted widespread forecasts of a 4-0 series whitewash in the hosts' favour.
"We didn't handle the Ahmedabad wicket as well but the others were all very different and we adapted well," said Cook.
"The bowlers have been brilliant and our batters have contributed big runs. Everyone in the squad can be very proud, especially after Ahmedabad and that heavy defeat.
"The guys who played a couple of games all made a difference and the amount of effort the guys have put in for me, I can't ask any more."
James Anderson was awarded the man of the match award after taking four for 81 in India's first innings and finished with 12 wickets in the series.
He came into his own during the third and fourth Tests by mastering reverse-swing after a relatively quiet start in India.
The 30-year-old always believed he would have a key part to play, refusing to rely on the spinners who normally prosper on the subcontinent.
"When we come over here, people think that spinners are going to get all the wickets but we knew that the seamers had a job to do over here," he said.
"We really wanted to show people we can do a job here and I really think we have.
"I've bowled better than I have before. Reverse-swing has been a key part of us doing well.
"We've really practised it in the nets and in the games we've had leading up to the series. I think we executed our plans really well in the game."
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