The group posted a 15.3% rise in group gross sales - which is boosted by its deal to handle online deliveries for Big Four supermarket Morrisons - to £312.4m for the 12 weeks to 21 February, while retail sales lifted 13.8%.
Ocado said it hit its weekly orders milestone since the end of its first quarter, despite ongoing tough trading in the grocery sector, which is gripped by a fierce price war with discounters Aldi and Lidl.
But the size of its average order slipped 2.9% to £111.41 during the first quarter in a sign of the pressures in the sector.
Tim Steiner, chief executive of Ocado, said: " We are pleased with the steady progress in our business, maintaining double-digit sales growth in a retail environment that remains challenging."
Its trading update comes amid concerns over the impending threat from US online giant Amazon after it struck a deal last month with Morrisons.
The tie-up will see Amazon offer ''hundreds'' of Morrisons products - including fresh and frozen food - through its food delivery service Amazon Pantry and its subscriber service Amazon Prime Now.
Duncan Tatton-Brown, chief financial officer at Ocado, insisted that the group welcomed Amazon's move into the UK fresh food sector.
He said: "We welcome any competition that grows the market.
"The more people shopping online, we think, the better for us."
Shares surged as much as 8% after the trading update beat expectations in the City, while investors also cheered Ocado's bullish outlook as it said it would "continue growing ahead of the online grocery market".
The stock has been under pressure in recent months, seeing hefty falls on the day that Amazon announced its deal with Morrisons last month, while there have also been concerns over the lack of any international tie-up for Ocado.
Mr Tatton-Brown said Ocado remained in talks with "multiple partners" over a potential overseas deal, adding that discussions were "progressing well".
Retail analyst Clive Black, at Shore Capital, praised a "sound" trading update.
But he said renegotiations with Morrisons over their partnership contract were "critical to Ocado's future".
FTSE 250-listed Ocado first signed a £170m contract with Morrisons in 2013, providing the Bradford-based supermarket with its first online delivery service.
They are renegotiating terms, with Morrisons last month announcing it had agreed in principle with Ocado to develop a store-picked offering - to extend the reach of Morrisons.com - and said it would take up space at Ocado's new customer fulfilment centre in Erith, Kent.