Gonzalez rose to head home an Estaban Paredas cross in the 75th minute to reward Chile's persistence, after the sOuth American side had wasted numerous chances.
Switzerland surpassed the record for the longest run without conceding a goal at the World Cup finals, but the Swiss were always under pressure after Valon Behrami was sent off for raising an arm to Arturo Vidal.
The result gives Chile their second successive victory following an opening 1-0 win over Honduras and leaves them top of Group H on six points ahead of a final game against Spain on Friday.
Switzerland, who beat the Spanish in their first game, can still qualify if they beat Honduras by two clear goals, or by a single goal and the other result goes their way.
GROUP H STANDINGS
Group H W D L F A GD Pts Chile 2-0-0 2:0 +2 6 Spain 1-0-1 2:1 +1 3 Switzerland 1-0-1 1:1 0 3 Honduras 0-0-2 0:3 -3 0