Stewart Haas Racing driver Harvick dominated the race's first stage and surged to a last-gasp stage three win on fresh tyres, using his track position at the start of the fourth stage to hold the lead and defend from nearest rival Suarez.
Both were able to hang on at the front despite having much older tyres than the pursuing Joey Logano, who pushed Harvick clear of Suarez on the final restart with two laps remaining.
Denny Hamlin opted for an identical strategy to his Joe Gibbs team-mate Suarez, staying out on old tyres to secure fourth place.
Hendrick Motorsports pair Chase Elliott and Jimmie Johnson finished fifth and sixth respectively, as Johnson charged from 19th late in stage three on fresh tyres after a pitlane speeding penalty.
Ganassi's Kyle Larson took seventh place on the freshest tyres of all, having triggered the final caution period when he was spun out by Logano.
Logano moved to the outside of Larson exiting Turn 4 while they battled for position, but the sidedraft effect made Logano's Penske loose and sent him against the wall before he rebounded back in the direction of Larson and sent him into a spin.
AJ Allmendinger finished eighth despite going a lap down in stage two, when he hit the wall and sustained damage to the right side of his Chevrolet. He qualified for the All-Star race by winning shorter Open race on Saturday, which runner-up Suarez also used to qualify by winning stage two in the earlier race.
Kyle Busch ran near the front for much of the race, but was caught out in a big accident during an overtime restart at the end of stage three.
That blocked Busch's path and inflicted minor damage on his Toyota, while Truex and Brad Keselowski were both eliminated - the latter running out of room before crashing into a spinning Truex.
Kasey Kahne completed the top 10 despite losing four laps when he took a solo trip in the wall while attempting to pass Suarez early in stage two.
Thanks to multiple late restarts, he made up laps through free passes, taking advantage of a late high attrition rate.
Alex Bowman had been the last of three cars which qualified under the earlier Open race, but he retired after spinning out and crashing into the wall on his own.