The Royals have won three in a row for the first time in six weeks, a stretch of success that has come after they had lost seven out of nine.
Lough singled in the second of the two Kansas City runs in the first, Gordon had a sacrifice fly in the second and both had an RBI during a three-run fifth that gave the Royals a 6-1 lead.
Gordon tripled in a run in the fifth and scored on a single by Eric Hosmer, after which Lough drove in Hosmer with a base hit.
Guthrie (10-7) gave up the only Baltimore run on five hits while striking out five in six innings.
The loss went to Miguel Gonzales (8-4), who surrendered five runs on eight hits in 4 2/3.