Trott knocked 143 and Bell 116 not out dug in to secure the required draw to take the series 2-1.
Only Trott’s wicket fell on day five, with Joe Root the other not out batsman on 20 when stumps were called early.
England wrapped up the series 356 runs ahead in the fourth Test, and didn’t attempt to push for a win.
It was a massive turn around for the tourists, who were beaten in the first Test by nine wickets but have dominated since.
The last time England won in India was David Gower’s side in 1984-85.
It was India’s first home series defeat since the 2004 Aussie side featuring Warne, McGrath and Ponting.
India’s insistence on preparing spin friendly wickets backfired, with England’s tweakers Graeme Swann and Monty Panesar outperforming their homeside counterparts, while James Anderson was the pick of the quicks.
The undoubted star of the series was Alastair Cook, but all of England’s batsman contributed.
England weren’t flying on day four, letting the host’s in when they fell to three for 94, but Trott and Bell ensured the result.
After Australia’s series loss to South Africa 1-0, England go to second on the England ICC Test rankings ahead of their tour of New Zealand in March.
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