The 1987 NCAA Division I-A football season ended with Miami winning its second national championship during the 80s in an Orange Bowl match-up featuring a rare No. 1 vs. No. 2 matchup between the top ranked Oklahoma Sooners and the Hurricanes.
Miami's first three games were against ranked opponents, in what was labeled as a rebuilding year, when after some late game theatrics by Michael Irvin against rival Florida State, the Hurricanes were 3–0, the national media started to take notice.
Oklahoma was also seen as quite the juggernaut, averaging 428.8 yards rushing per game with their potent wishbone offense. Miami was able to hold Oklahoma to just 179 yards on the ground, winning the game 20–14.
Also having notable seasons were Syracuse, LSU and Florida State. Syracuse finished the season 11–0–1 and ranked No. 4 after a controversial Sugar Bowl game in which Auburn kicked a late field goal to end the game in a tie. LSU went 10–1–1, ending the season ranked No. 5. This was LSU's first ten win season in 26 years and their highest ranking since 1961.
Florida State finished ranked No. 2, their only loss to Miami, and began a streak of 14 years where FSU either finished in the top 5 or played for the national championship. The Seminoles beat Rose Bowl champion Michigan State and SEC champion Auburn on the road and beat Nebraska in the Fiesta Bowl.
This would be the first of two years SMU would not field a team due to the NCAA's death penalty. Taken from https://en.wikipedia.org/wiki/1987_NCAA_Division_I-A_football_season

Final Stats:

AP Poll Summary
School	Conf	Final
Miami (FL)	Ind	1
Florida State	Ind	2
Oklahoma	Big 8	3
Syracuse	Ind	4
Louisiana State	SEC	5
Nebraska	Big 8	6
Auburn	SEC	7
Michigan State	Big Ten	8
UCLA	Pac-10	9
Texas A&M	SWC	10
Oklahoma State	Big 8	11
Clemson	ACC	12
Georgia	SEC	13
Tennessee	SEC	14
South Carolina	Ind	15
Iowa	Big Ten	16
Notre Dame	Ind	17
Southern California	Pac-10	18
Michigan	Big Ten	19
Arizona State	Pac-10	20
Top 10 NFL Players Drafted in 1988
Rnd	Pick	Tm		Pos	College/Univ
1	19	MIN	Randall McDaniel HOF	G	Arizona St.
2	40	BUF	Thurman Thomas HOF	RB	Oklahoma St.
1	11	DAL	Michael Irvin HOF	WR	Miami (FL)
1	6	RAI	Tim Brown HOF	WR	Notre Dame
2	30	PHI	Eric Allen	DB	Arizona St.
2	44	PIT	Dermontti Dawson HOF	C	Kentucky
1	2	KAN	Neil Smith	DE	Nebraska
3	80	SFO	Bill Romanowski	LB	Boston Col.
2	41	DAL	Ken Norton	LB	UCLA
3	74	NYJ	James Hasty	DB	Washington St.