The tech giant's strategy of charging more for its phones has paid off, with revenues jumping in the last three months despite relatively flat sales.
Revenues rose 20% to $62.9bn year-on-year, and profits rose 31% to $14.1bn.
But a warning of possible weaker sales in coming months sparked a share price slide after official trading ended.
The sell-off accelerated after Apple said it would stop disclosing the number of units sold.
Apple executives defended their decision, arguing that the figures are no longer good indicators of the firm's financial health.
Analysts, however, warned that outsiders may view it as a move that masks less sunny performance.
The total number of smartphones sold by all makers globally declined for the first time in 2017.
But Apple's strategy of charging higher prices for its phones has helped it to shrug off flagging demand.
The firm sold 46.9 million iPhones in the quarter to end-September, a modest rise on the 46.7 million sold for the same period last year.
The California-based company is also making more money from "services" such as the App store, Apple Music and Apple Pay. Services revenue hit a record $10bn in the quarter.
For the firm's full 2018 financial year, profits increased 23% to $59.5bn, as revenue rose 16% to $265.5bn.
"I can reassure that it is our objective to grow unit sales for every product category that we have," Apple's chief financial officer Luca Maestri told financial analysts.
"A unit of sale is less relevant today than it was in the past."
Despite the record figures, shares in the firm sank in after-hours trading, falling by 4% and then by more than 7%. They quickly started to rebound, lifting the firm's market value back above $1tn.
The decline was blamed in part on a disappointing forecast for the important Christmas season.
Apple said it expects sales of $89bn to $93bn for the quarter that ends 31 December, against Wall Street's $93bn forecast.
It posted sales of $88.3bn in the quarter last year.
Chief executive Tim Cook said that Apple is "seeing some macroeconomic weakness in some of the emerging markets" such as Turkey, India, Brazil and Russia.
He said some of that is due to currency fluctuation.
Chief financial officer Luca Maestri said Apple also faces some supply uncertainty related to the roll-out of its latest products.
The firm, which relies on China for manufacturing, is at risk as trade tensions between US and China rise, though its products have so far been spared from tariffs.
Mr Cook said he remains optimistic that the two countries will resolve their issues.
So far, Apple's business has not been affected he added, pointing to a 16% revenue rise in its Greater China region in the most recent quarter.
Apple's App store has felt the impact of a "moratorium" on Chinese approvals for new games, but that is a domestic issue, he added.