Tre Davis starred for the Hammond defense in the second half, recording four tackles for loss, including a pair of quarterback sacks.
Hammond was coming off of a disheartening, 14-13, overtime loss to Centennial last Saturday, and also lost to Reservoir, 21-20, earlier this season.
"It's been a hard luck season for these guys, we're 3-5 with a lot of close games," Hammond coach Dan Makosy said. "We've just been coming up on the short end ... good efforts get old after awhile, they're still losses.
"The county is very balanced this year," Makosy added. "Howard County is the toughest football in the state right now."
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Centennial shut out visiting Marriotts Ridge (2-6), 13-0, to improve to 3-5.
The Eagles were led on offense by Walter Fletcher, who rushed for 121 yards and a touchdown on 28 carries.
Michael Price (32 rushing yards) scored Centennial's other touchdown when he recovered a fumble and returned it 20 yards for the score.
Both touchdowns came in the second quarter. Damon Reaves caught two passes from Patrick McKinnis for 37 yards.
Centennial's last shut out came last Oct. 29 at Marriotts Ridge. It was Centennial's only win last season.
After beating Hammond last Saturday in overtime, the Eagles have now won back-to-back games for the first time since 2010.
With three wins, Centennial is having its best season since 2009, when it finished 4-6.