Archie Goodwin added 18 points and Nerlens Noel 11 as the Wildcats (8-3) won their fourth straight before a season-high 24,271 at Rupp Arena. Kentucky also improved to 12-0 against Marshall.
Kentucky's final tune-up before next Saturday's showdown at fifth-ranked Louisville saw the Wildcats shoot just 42 percent (29 of 69) but benefit from even worse shooting by the Thundering Herd, who hit 29.5 percent (18 of 61).
Harrow, making his second straight start at point guard, helped lift Kentucky from its sluggish start with 11 first-half points and two assists. He surpassed his previous career high of 20 two years against South Carolina Upstate while playing for North Carolina State.
Elijah Pittman had 17 points and Dennis Tinnon 14 for Marshall (7-6).
Though Kentucky had rolled over its last three opponents by an average of nearly 33 points coming in, coach John Calipari has wanted more from his players and has pushed them hard in twice-daily workouts during the semester break. More than anything, he has wanted his players to communicate more on the floor.
Finishing games has been an issue for Kentucky as well but starting was the initial problem against a Marshall team that entered the game with seven players at least 6-foot-8 and owning the nation's 22nd-best rebounding average (41.3) The Wildcats still managed to get an early edge thanks to one of the smallest players on the floor, the 6-2 Harrow.
His three layups helped stake Kentucky to a 10-7 lead during a competitive first 10 minutes featuring five ties and six lead changes. Marshall stayed close thanks to D.D. Scarver and Pittman, junior college transfers who have recently carried the scoring with top scorer DeAndre Kane out indefinitely with a right-hand injury.
In the early going the duo combined for 16 points to give Marshall a brief 20-18 lead.
Harrow quickly tied it with a bank shot and followed with a 3-pointer that put Kentucky back ahead 23-20. Besides providing nearly half of the Wildcats' offense at that point, he was also more active than his teammates.
Fortunately for Kentucky, Marshall scored just two baskets over the final 8:17 of the half. The Wildcats picked up the pace a bit on both ends, with Noel blocking a shot on one Marshall possession before following with a steal and layup for a 31-22 lead.
Julius Mays' two free throws gave Kentucky a nine-point lead at intermission despite shooting 35 percent (13 of 37). Cold-shooting Marshall was just 28 percent (8 of 29).
The Thundering Herd scored the first seven points of the second half to close within 33-31, but consecutive layups by Harrow keyed an 8-1 run and stretched the lead to 41-32. Marshall went cold again, with Chris Martin sinking its only basket over nearly 7 minutes, during which the Wildcats pulled away with a 21-5 run.
The Wildcats played without reserve guard Jon Hood, who sat out with an upper respiratory illness and was not on the bench.
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