The paper, which began the giveaway of famous paintings in mid-July, shifted 250,761 copies during the month compared with 241,660 in June. However, its May figure was 257,226 before its circulation dropped more than 6%.
With the escalation of hostilities in the Middle East, readers may also have turned to the paper for veteran correspondent Robert Fisk's take on events.
The editor Simon Kelner said both were factors in the paper's improved performance.
"What has been important in our rise is a big running news story in the Middle East, and having Robert Fisk, the most celebrated Middle-East correspondent covering it. Obviously this translates into more sales," he said, also acknowledging that the giveway had been very successful.
The Independent's success may have harmed the Guardian, which lost 2.52% of its circulation, or almost 10,000 copies, to record 370,612 for July.
In a month dominated by headlines about Lebanon, readers gravitated away from the quality end of the market and towards the tabloids.
The Daily Telegraph only lost 0.3% from June, but that was sufficient to finally send its circulation below 900,000 to 897,416 copies. The Times will be celebrating anyway, but also enjoyed a 1.62% rise to 667,496.
No such luck at the Financial Times, which fell sharply by 3.87% to 423,548.
In the mid-market, the Daily Express fell 1.37% to 833,145 while the Daily Mail clawed back to where it was in May with a 2.09% rise to 2,389,236.
Among the tabloids, The Sun shone with a 1.87% increase to 3,207,430, which is its best figure for at least six months. Unusually, it and the Mirror had a good month, with the latter up 1.49% to 1,660,151. The Daily Star lost 0.79% to 797,132.
For other daily papers, the picture was gloomy. London's Evening Standard, soon to bear the brunt of News International's launch of its freesheet, thelondonpaper, in September, was down 2.88% to 300,993.
Scotland's quality press sank past psychologically important levels, with The Herald going below 70,000 and The Scotsman below 60,000.
The Racing Post lost 6.52% on June to 71,146 and its six-month average figure was down 7.38% year-on-year. It is hard to tell how much The Sportsman has been responsible for this decline, as it again did not give an ABC figure. It has its own worries, with a meeting to decide its future scheduled for Tuesday.
Like the daily market, the national Sunday market has returned mixed results. The Sunday Mirror was the best performer up 6.05% to 1,502,414 and stablemate the People also had a good month up rising 2.40% to 840,860. Red top rival the News of The World was up 0.33% to 3,482,856, remaining the UK's best-selling Sunday title. The Daily Star Sunday was down marginally by 0.59% to 403,824.
Like its daily edition The Independent on Sunday had a good July, up 2.84% to 216,175. The Sunday Telegraph did well too, rising 1.65% to 656,055 -- making these two the only quality national Sunday titles to register an improvement.
The Sunday Times was down of 0.42% to 1,308,604 and The Observer was down 2.75% to 457,806.
In the mid market the Mail on Sunday registered a sharp fall, dropping 4.09% to 2,221,338. Bad news as well for the Sunday Express, which was down 3.98%.
Scotland on Sunday continued an alarming decline, dropping 6.54% to 67,049 while the Sunday Herald fell 3.31% to 50,723. The Sunday Mail was down 0.73% to 517,609, making a poor month of it for the Scottish Sundays.
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