Overall sales were up by 7.1% in the six weeks to 7 January, the firm said.
The UK's second largest supermarket group, which also includes Argos, said it now expected annual profits for the year to March to be towards the upper end of its previously guided range of between £630m ($765.3m) and £690m.
Underlying pre-tax profits for its 2021-22 financial year, came in at £730m.
Sainsbury's said early Christmas shopping helped sales jump over the latest quarter as shoppers looked to spread the cost of the festive season.
Chief executive Simon Roberts said: "We delivered the best possible Christmas for customers as millions of households managed their budgets differently, hosting larger gatherings again and treating themselves at home."
The retailer said people were keen on getting festive snacks and drinks as well as taking advantage of deals.
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"Customers shopped early, buying Christmas treats and fizz more than once and looked for deals, taking advantage of Black Friday and other seasonal offers,” Roberts added.
The cost of living is rising at its fastest pace in 40 years, with many UK households struggling with rising food prices.
The supermarket remains "cautious" on the outlook for consumers.
"We understand money will be exceptionally tight this year, particularly as many people wait for Christmas bills to land," Roberts said.
The group said sales growth was driven by rising prices while volumes had remained "resilient". It also said customers watching the FIFA World Cup at home helped increase sales.
Sainsbury's highlighted that profits will be boosted by the firm’s finance costs, which are set to be £15m lower than previously expected.
The improved profit guidance comes as supermarket margins come under pressure from soaring food inflation and efforts to keep a lid on price increases for customers.
Sainsbury's share price dropped around 2% on Wednesday despite its announcement of record Christmas sales.
Sainsbury's stock fell 21% last year and investors may be concerned about tightening margins as the supermarket battles with discounters Aldi and Lidl to maintain its market share.
Charlie Huggins, head of equities at Wealth Club, said: "This is a solid performance from Sainsbury's with the group raising its profits and cash guidance for the year, against an intensely competitive market backdrop.
"It seems that UK shoppers indulged in one final sales splurge in the run up to Christmas, benefitting Sainsbury's and its peers. However, with the slowdown in consumer spending yet to really bite, it's likely the environment will get tougher."
Richard Hunter, head of markets at Interactive Investor, said: "Sainsbury's has guided that the full-year underlying pre-tax profit will be towards the upper end of the £630m to £690m range previously advised. This would nonetheless be a decline from the previous year’s showing of £730m and underlines the scale of the challenges which show few signs of abating...
"The market consensus of the shares has recently deteriorated to a sell, with Tesco remaining the preferred play, although this could be subject to upgrades given the general success of the latest quarter.”
In November, Sainsbury’s confirmed it will invest a further £50m into pricing by March, taking overall investment to improving prices to £550m.
Orwa Mohamad, retail analyst at Third Bridge, said: “Sainsbury’s focus on everyday low prices and its Aldi price-match scheme only mitigates market share losses. Meaningful levels of growth look very difficult over the next 12 months.
“The only way Sainsbury’s can really lighten the impact of the discounters is by playing to its strengths around on product range, non-food items, convenience, and being competitive on the key basket items. For now, discounters like Aldi or Lidl offer comparatively limited ranges.
“Sainsbury’s is fighting a rearguard action to maintain its gross profit margins by carefully passing on extra costs to customers. However, every day that the cost of living crisis persists lends greater strength to the likes of Aldi and Lidl as their store numbers grow and the stigma of using discounters melts away.
“Our experts say Sainsbury’s could do more to improve operational efficiency around range rationalization and simplifying processes. They are lagging behind Tesco (TSCO.L) in these respects.”