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The benchmark index was up 56.96 points at the close of trading on Wednesday, taking it to 5,004.30.
Royal Dutch Shell, BG Group, Cairn Energy and BP climbed by as much as 4.2 per cent after the price of oil rose over $71 (£42.9) per barrel.
In the travel sector, there were gains for British Airways and Thomas Cook, while banks also performed well, with HSBC, Barclays, Royal Bank of Scotland and Standard Chartered all seeing their share price rise.
However, Lloyds Banking Group was one exception, ending 0.7 per cent lower.
Market analyst Nick Serff said that while the climb was "important", it may not last.
He noted that "a stay above 5,000 may be short-lived" due to the fact that many investors began adding short positions to their portfolios following the increase.
