Wasps took control in the early stages, led by captain Laurence Dallaglio, the visitors dominated the bulk of possession and took the lead within three minutes through a penalty kick by Van Gisbergen.
But Wasps failed to convert their following efforts into points with winger Josh Lewsey coming close, only to be shut down by some desperate Bath defence.
Tempers began to flair, with Bath hooker Jonathan Humphreys and his team-mate Andy Beattie both throwing punches, but it was the hosts who were awarded a chance to draw level when Bath scrum-half Martyn Wood and England lock Simon Shaw got involved in a tussle.
Regular Bath fly-half Olly Barkley, who had moved to centre for the match, made no mistake, but Wasps again took the lead through a fantastic counter-attack following a later missed penalty attempt by Barkley.
Shaw sent ex-Bath wing Tom Voyce clear, and the winger put through a well-placed kick to be caught by Van Gisbergen, who sprinted clear and touched down. The Wasps fullback stretched the lead to 10-3 with the conversion.
Barkley, however, soon closed the gap with another penalty shortly before the break for the hosts to go into half-time trailing by just four points.
Ireland centre Kevin Maggs took over from Chris Malone in the midfield after the break, leaving Barkley free to move back to fly-half, but another missed penalty by the latter left Wasps four points clear, despite Bath applying all sorts of pressure.
Wasps continued to be penalised, but Barkley pushed a third attempt wide not long after and it proved to be the end of Bath's challenge as the visitors managed to hold on. Lewsey then seemed to have wrapped the game up after intercepting a pass by Barkley racing 60 metres to the Bath line.
But White took play all the way back to the Wasps' 22 for an earlier knock-on much to the dismay of the visitors. Bath, however, failed to take advantage of the decision with Wasps holding out for the win.
For Bath:Pens: Barkley 2
For London Wasps:Try: Van Gisbergen Con: Van Gisbergen Pen: Van Gisbergen