Wales international fly-half Robinson converted an early try from Sam Jones - Wasps' only one of the match - and then booted five penalties to help hold off Bayonne.
The victory avenged Wasps' defeat in France last weekend and moved them one point clear of Bayonne at the top of Pool Three with two games to play.
In the other match in the pool, Nicolas Sanchez took his personal tally in the back-to-back games between Bordeaux-Begles and Rovigo to 21 as he scored all his side's second-half points to bag the French Top 14 outfit a 15-10 home win.
After winning 31-7 in Italy last weekend, it was a surprise to see Bordeaux-Begles trailing 10-5 at the break.
Hooker Boris Bethery gave the home side a flying start with a try after only eight minutes, but Italian international wing Roberto Pedrazzi hit back with one of his own midway through the half. Samuele Pace added the conversion and then fly-half Davide Duca dropped a goal moments later.
That left Bordeaux-Begles needing to up their game in the second half and their own number 10, Sanchez, ensured they did that as he cut the gap to two points with a penalty before crossing for a try which he also converted.
That gave the French side a five-point lead with 30 minutes to go and they successfully negotiated the remainder of the game without ever looking like gaining another bonus point.
Despite suffering their fourth successive loss, Rovigo at least picked up their first point of the campaign with a losing bonus.
Stade Francais heaped more pressure on Worcester Warriors in Pool One as they comfortably completed the double over Italian outfit Crociati to move nine points clear at the top.
Worcester face Bucharest Wolves at Sixways on Saturday afternoon and must pick up another five points if they are to stay in touch with the French side and give themselves any chance of overturning their home defeat by the Parisians in round one.
France lock Pascal Pape was the man who brought up the bonus point for the home side with the second of his two tries after 50 minutes and Michael Cheika's men ended up with seven scores in a 45-3 win.
In Pool Five, Brive set Sale Sharks a tough target as they made it a bonus-point double over Spanish champions La Vila with a 38-13 triumph on home soil. Fly-half Benjamin Caminati converted four of his side's five first-half tries and ended with a match tally of 13 points.
The former Heineken Cup winners were 33-3 ahead at the break and appeared to ease off in the second half having secured their bonus point and they now have a firm grip on top spot, lying eight points clear of second-placed Sale, who entertain Agen on Sunday.
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