Mendes struck in the 40th minutes after a lovely three player move between Dan Gleeson, Jason Lee and David Pipe, whose right-wing cross was converted with aplomb by Mendes.
Stockport had started the brighter of the two sides and forced one of the best saves of the entire game from Kevin Pilkington as early as the 16th minute.
Liam Dickinson skipped passed Alan White before unleashing a powerful drive which the alert Pilkington turned round his right-hand post.
Notts threatened again immediately after scoring and were unlucky not to double their lead.
Lee flicked the ball against the upright from short range with John Ruddy seeming to be beaten.
But Stockport stormed back and the last save of the half was made by Pilkington this time to keep out Jason Taylor's low drive.
After their two half-time substitutions the visitors stepped up a gear and severely tested the Notts backline.
But the Notts defence, with Mike Edwards in outstanding form, held firm to such an extent that for all Stockport's pressure, Pilkington was barely troubled.
The nearest to another goal was supplied by Notts in the 73rd minute.
Taking an astute pass from Ian Ross, Gleeson surged forward for all of 35 yards before delivering a low drive which whistled wide of Ruddy's left-hand post.
After that Stockport continued to press for an equaliser but time and again were held up by steadfast defending by Notts.
The victory stretched Notts' unbeaten home record to six, but was rewarded by the poorest Meadow Lane gate of the season.