But Bolton threatened an equaliser with Sam Johnstone making terrific saves to deny Sammy Ameobi and Jason Lowe as Albion kept just a fourth clean sheet in the league.
West Brom were denied a penalty when Mason Holgate’s cross struck Andrew Taylor’s arm while Dwight Gayle clipped the bar. The substitute Field, on for the injured Brunt, clinched victory by scoring his second first-team goal after a defence-splitting pass from Rodriguez.
Bolton Wanderers (4-2-3-1): Alnwick; Olkowski, Hobbs, Beevers, Taylor; Lowe, Murphy (Buckley 69); Ameobi, O’Neil, Noone (Pritchard 82); Donaldson (Magennis 69).
Substitutes not used: Matthews (g), Wilson, Wheater, Connell.
Booked: Olkowski, Donaldson.
West Bromwich Albion (4-3-3): Johnstone; Holgate, Dawson, Hegazi, Gibbs; Harper (Adarabioyo 90), Barry, Brunt (Field 26); Robson-Kanu (Sako 85), Rodriguez, Gayle.
Substitutes not used: Bond (g), Bartley, Leko, Hoolahan.
Booked: Holgate, Barry.
Referee: David Webb (County Durham).