Argentine Mayer was rewarded for his maiden ATP World Tour title, which came with a win over David Ferrer in Sunday's final, by jumping 19 places to 27th in the world.
Despite his loss in the final of the ATP 500 clay-court event, Ferrer moved up one place to sixth in the rankings.
It meant Canadian Milos Raonic slipped to seventh in the only change to a top 14 headed by Serbian world number one Novak Djokovic.
Italian Fabio Fognini, champion in Hamburg last year, fell five places to 20th after only reaching the second round in 2014.
Claro Open Colombia champion Tomic is 70th in the world after moving up 54 places on the back of his win in Bogota.
German Alexander Zverev, the 17-year-old who reached the last four in Hamburg, is at 161 after rising 124 places.
In the WTA rankings, which Serena Williams is still clear on top of, Danish Istanbul Cup winner Caroline Wozniacki sits 13th, up two places.
Swedish Open winner Mona Barthel is into 42nd, up from 61st.