"We expect our high-level performance to continue," said Donnie Smith, the Tyson chief executive, heralding bright prospects in the next financial year too.
"We intend to build on our momentum to generate more growth in fiscal 2017."
The group forecast a 1% rise in sales in its next financial year, combined with margins expected to stay at about current-year levels in its main business divisions.
The comments came as Tyson unveiled a 41% jump to $484m in earnings for the three months to July 2 - equivalent to $1.21 per share, ahead of the $1.06-per-share result that Wall Street had expected.
Although sales fell by 6.4% to $9.40bn, a reflection of the dent to beef values from higher supplies, operating profits rose 36% to $767m thanks to the boost to margins from lower prices of bought-in cattle and, in poultry, lower feed costs for the group's own production operations.
"All operating segment results were in, or above, their normalised operating margin range, with the chicken segment delivering a record 13.9% return on sales," Mr Smith said.
Operating profits in chicken rose 21% to $380m, underlining its position as by far Tyson's biggest earning business, although the pork business achieved a quicker growth in profits, of 91% to $122m.
'More favourable market conditions'
The beef division reported its highest profits in nearly two years, staying in the black for a third quarter, after losses in all reporting periods of last year.
"Operating income increased due to more favourable market conditions, associated with an increase in cattle supply which resulted in lower fed cattle costs."
Tyson forecast a rise of 2-3% in its 2017 fiscal year in US supplies of fattened cattle, leaving "generally adequate supplies" in areas the group operates in.
US chicken and hog supplies will also rise by 2-3% in the next financial year.