Unbeaten Hoffenheim now have 19 points, four behind leaders Bayern Munich, while Hertha, who had goalkeeper Rune Jarstein to thank for a string of superb saves, are fifth on 17.
Cologne are up to fourth courtesy of French forward Anthony Modeste's first Bundesliga hat-trick in a 3-0 win over bottom side Hamburg that takes them on to 18 points.
Hoffenheim needed 20 minutes to settle but then took control, rattling the crossbar with a Pavel Kaderabek header after Jarstein had denied Lukas Rupp from close range.
The hosts broke the deadlock in the 31st minute with Suele's header and were rarely threatened, apart from a Vedad Ibisevic effort which was parried by keeper Oliver Baumann.
Norwegian Jarstein thwarted Hoffenheim's strikers several more times but could do nothing to prevent their first defeat in October.
Cologne's Modeste grabbed a second-half treble, after Hamburg's Bobby Wood was sent off in the 58th for elbowing an opponent, to become Bundesliga top scorer on 11 goals.
Hamburg, still without a win this season, remain stuck on two points after their seventh defeat in nine matches.
Bayern are top on 23 points after Saturday's 3-1 win at Augsburg, with RB Leipzig two points behind in second following their 2-0 win at Darmstadt 98.
(Reporting by Karolos Grohmann; Editing by Ian Chadband and Ken Ferris)
