Apple (AAPL) blew past all but the most optimistic estimates Tuesday, reporting third-quarter earnings of $3.51 per share on a record $15.7 billion in revenue.

That Apple was able to top sales for even its Christmas quarter — traditionally its strongest — was remarkable. Apple executives attributed it to the addition of a new product line — the iPad — which brought in an additional $2.2 billion.

Net quarterly profit was $3.25 billion, up 77.6% from the same quarter last year.

“It was a phenomenal quarter that exceeded our expectations all around, including the most successful product launch in Apple’s history with iPhone 4,” said Steve Jobs, in a prepared statement. “iPad is off to a terrific start, more people are buying Macs than ever before, and we have amazing new products still to come this year.”

Wall Street was anticipating earnings of $3.11 per share on revenue of $14.75 billion, according to a survey of analysts by Thomson Financial.

Apple’s guidance, usually laughably conservative, was surprisingly positive: Earnings of $3.44 on revenue of $18 billion in the quarter than ends in September.

Apple’s shares, which had fallen as low as $240.01 in early trading, closed at $251.89, up $6.31 (2.57%) for the day. The stock added nearly 9 points in after-hours trading.

The stock, which had reached as high as $279 in June, has been under pressure amid concerns that negative publicity surrounding the iPhone 4’s external antenna could affect fourth-quarter sales.

But there was no sign of slackening demand in Tuesday’s results. iPhone sales were up 61% from Q3 2009.

Here are the numbers:

• Total sales: $15.7 billion, up 61.3% year over year
• Earnings: $3.51 per share, up 74.6%
• Profit: $3.25 billion, up 77.6%
• Mac sales:  3.47 million units, up 33%
• iPhone sales: 8.398  million units, up 61.25%
• iPod sales: 9.4 million units, down 7.9%
• iPod touch sales: up 48%
• iPad sales: 3.27 million, slightly below the Street’s consensus
• Retail store sales: $2.58 billion, up 73%, in 293 stores
• Cash and marketable securities: $45.8 billion, up $4.1 billion from Q2
• Gross margin: 39.08%, down from 41.7% last quarter
• Guidance for the third fiscal quarter: Revenue: $18 billion, EPS: $3.44, Gross margin: 35%

Apple’s press release is available here. A webcast of the conference call will be available for two weeks here. Seeking Alpha has the transcript here.

See also:

• Apple’s earnings: 5 numbers to watch
• The Street awaits Apple’s Q3 earnings
• Let’s talk about the Mac for a change
• How many iPhones did Apple sell in Q3?
• How many iPads did Apple sell in Q3?
  
• How many iPods did Apple sell in Q3?

[Follow Philip Elmer-DeWitt on Twitter @philiped]