Palmer was involved in all three Walsall goals and generally had a fine match as his performance lifted the Saddlers up the table.
With only two points from their previous five games Walsall halted their recent rapid decline following a good start to the season.
They responded with a positive first-half performance which effectively killed off the Cobblers.
Their failure to take their chances has cost them dearly in recent weeks, but on this occasion they grabbed two well-taken first-half goals to seal a good win.
Palmer set the tone with his first ever goal for the Saddlers when the former Wycombe winger collected a pass from skipper Stephen Hughes, cut in from the left and hammered his shot into the roof of the net.
This goal lifted Walsall and Northampton's defence was breached for a second time in the 31st minute when Anthony Gerrard scored with a glancing header from Palmer's right-wing corner.
Northampton played some neat attacking football but there was no real penetration. Andy Holt was a key player on Northampton's left flank but the Cobblers failed to prosper from his probing play.
In the second half manager Stuart Gray sent on Liam Dolman in an attempt to give his front players more finishing power.
But the Saddlers were under no real pressure and weathered all the attacks mounted against their defence.
Only a desperate clearance by Jason Crowe prevented Michael Ricketts notching a goal, but in the 61st minute a Palmer effort was blocked and cannoned skywards.
Goalkeeper Frank Fielding was beaten to the ball by Troy Deeney and his header rolled into an empty net.
Northampton continued to battle and were rewarded when Leon Constantine headed home after Ryan Gilligan's effort rebounded to him off the bar in the 68th minute.
Only the bar prevented Giles Coke obtaining a second goal ten minutes from time when his long-range effort deserved a better fate.