The two brands took a 7.1% share over the 12 weeks to January 5 compared to 5.8% the year before, with Aldi increasing total sales to more than £1 billion.
Data from Kantar Worldpanel confirmed Morrisons as the big loser in the sector because it was the only business to see a fall in total sales. Its delay in launching an online operation saw it miss out on a web ordering surge that propped up its rivals.
Total grocery sales were up 2.9%, but Waitrose again showed its success in attracting higher-spending shoppers by beating the figure with a 6.4% improvement and taking its market share 0.1% higher to 4.8%.
Tesco and Sainsbury's also muscled in on the premium market as their Finest and Taste The Difference brands strongly outperformed their value ranges. The two retailers were also buoyed by double-digit growth in their convenience stores.
Of the big four grocers, only Sainsbury's held its own in market share. It stayed at 17.1%, which helped it draw level in the rivalry to be Britain's second biggest supermarket with Asda, which saw its slice go from 17.5% to 17.1%.
Tesco, still the largest by a distance, fell from 30.4% to 29.6% as it managed only a 0.2% increase in sales.
But Morrisons dipped from 12% to 11.5% as total sales fell 1%. The Bradford-based retailer, which launched its online deliveries just days ago, missed out on the UK's 22% increase in internet grocery sales over the period, with 15% of households placing orders.
Aldi's market share rose from 3.1% to 4% as sales rose 29.4% to £1.08bn in the period. Lidl's share was up from 2.7% to 3.1%, with revenues up 17.5% to £528 million.