Mitchell, the leading scorer for the Mountaineers (8-2), recovered after being held to a total of eight points in his previous two games. His 3-pointer with 7:45 left in the second half ignited a 19-8, game-ending West Virginia run.
Mitchell finished 5 of 14 from the floor and 3 of 8 from behind the arc.
The Vikings (12-1) drew within seven points on Trevon Harmon's 3 with 3:50 left. But two Cam Thoroughman free throws, followed by Jones' 3-pointer with 2:45 remaining, quelled any chance of a Cleveland State comeback.
Norris Cole, who led Cleveland State with 19 points, tied the score at 55 with 8:30 to go in the second half, but 3-pointers by Mitchell and Jones on consecutive possessions made it 61-55 and sent West Virginia on its way.
Jones scored all but two of his points in the second half.
Cleveland State, off to its best start in school history, was looking to become the first NCAA Division I school to win its first 13 games this season and to avenge last season's final-second loss to West Virginia in Cleveland.
The Vikings have all five starters back from last season's 16-17 squad, but those veterans couldn't match the Mountaineers' timely shooting and opportunistic defense down the stretch.
West Virginia, which fell behind by double digits in the first half of a 64-61 win over Duquesne last Sunday, struggled again in the first half. It failed to find consistency at either end of the floor against Cleveland State but managed a four-point halftime lead after trailing by four, 22-18, with 9:39 until halftime.
The Mountaineers led by as many as nine points in the first 4:02 of the second half before Cleveland State came roaring back.
Down 47-38 with 15:58 to go, the Vikings scored eight straight points to come within a point but couldn't get over the hump.
The Mountaineers forced three turnovers and the Vikings didn't score a point during a span from the 8:30 mark of the second half until 3:50 remained.
John Flowers added 10 points and three blocks for West Virginia.
The Mountaineers shot 47.4 percent from the floor, while the Vikings managed only 41.7 percent.