Chevron reported third-quarter profits of $1.28bn, and while that was down from $2.04bn last year as a result of lower oil prices, cost cutting meant the results were ahead of forecasts.
The Dow Jones fell 7 points to 18,161.9 despite Chevron rising almost 4%.
The wider S&P 500 shed 6.6 points to 2,126.4.
The tech-focused Nasdaq ended the day down almost 26 points at 5,190.5.
Shares in online retail giant Amazon ended down 5.1% after the company said profits in the fourth quarter were set to be much lower than expected because of increased investment.
Amazon forecast operating profit of between zero and $1.25bn in the quarter, compared with analysts' expectations of $1.62bn.
Tyre maker Goodyear suffered an 8.7% slide in its shares after reporting a 8.1% fall in third-quarter revenues to $3.85bn and cutting its full-year profit forecast.
(Close): Better-than-expected results from oil giant Chevron failed to keep the Dow Jones in positive territory.