The visitors led in the eighth minute when Zakaria Labyad capitalised on some slack defending but Breda were soon back on terms from the penalty spot, Jordy Buijs slotting into the bottom corner.
The decisive goal arrived in the 26th minute as Mike Havenaar poached a close-range finish from Christian Atsu’s cross.
Twente will regain second place - the final UEFA Champions League qualifying spot - if they can beat Go Ahead Eagles on Sunday, while PSV stayed in touch with the chasing pack behind leaders Ajax courtesy of a 1-0 home win over Utrecht.
The scoreline was not reflective of the hosts' domination as a clutch of first-half chances went begging but the decisive moment arrived five minutes after the restart - Jurgen Locadia's opportunist strike making it six wins in a row for the Eindhoven club.
At the other end of the table, Roda JC ensured NEC replaced them in last place with a 3-1 triumph over their fellow strugglers.
Berry Powel and Guus Hupperts capitalised on a mistake from NEC goalkeeper Karl-Johan Johnsson for the latter to open the scoring against the run of play,
Hupperts would complete a brace after Marc Hocher netted a second-half free-kick, while NEC's Michael Higdon reduced the arrears with half an hour remaining.
USA striker Aron Johannsson netted a double as AZ recorded a second 4-0 win in as many weeks, with Heracles Almelo - now four points above the drop zone - on the receiving end.
Heerenveen boosted their own top four hopes with a 3-0 win at home to PEC Zwolle. Bilal Basacikoglu, Rajiv van La Parra and Alfred Finnbogason were the men on target.
