The UK's third-largest supermarket said it marked a fifth consecutive quarter of "positive growth" and that it had done better than its rivals for the first time in four years.
It said if Easter had fallen within the second quarter this year, its performance would have been even better.
Asda said targeted price investment, a 13.2% rise in online grocery sales and a 24.9% increase in its clothing and homeware brand George - all helped sales.
It added that better food sales volumes and "strengthening performance in non-food categories" also gave it a boost.
Chief executive Roger Burnley said the results showed "continued momentum for 2018 and this is the first quarter we have outperformed the market since 2014".
"We remain focused on delivering our strategic priorities and investing in the areas that matter most to our customers - innovation in our own brand, lowering prices and in continuously improving our shopping experience both in store and online," he said.
During the three-month period, the firm expanded its own-brand vegan range and launched its own-brand gin selection.
The Walmart-owned group is in the process of merging with Sainsbury's - the UK's second-largest supermarket.
The proposed £15bn tie-up has received a hostile reaction from MPs, who accused bosses in June of "talking baloney" over the effects such a deal would have on suppliers.
The chains have said the merger - which is being investigated by the Competition and Markets Authority - would allow them to pass on a 10% reduction in costs to shoppers.
Sainsbury's reported a slowdown in sales growth earlier this month, saying like-for-like sales were up 0.2% in the three months to the end of June.