Meath claimed five of the final six points at Dr Cullen Park as they advanced to the Leinster SFC quarter-finals.
Wicklow raced into a 0-05 to 0-00 lead after 14 minutes, but the Royals responded strongly despite an injury to captain Seamus Kenny. Wicklow still led by 0-08 to 0-07 at the break, yet Graham Reilly fired over four points for Meath on the restart.
An injury to skipper Leighton Glynn and a second yellow card for James Stafford hampered Wicklow's comeback bid.
There was just one change made to the line-ups that were announced in midweek with Stephen Byrne replacing Michael McLoughlin in the Garden County defence.
Wicklow had not beaten Meath in the Leinster Championship since 1957, but hopes were high in the county that the recently-crowned Division 4 champions could cause an upset.
Harry Murphy's charges impressed in the opening stages and rattled off five points with John McGrath, Tony Hannon and Stafford all landing early scores.
Meath were dealt a major blow during this Wicklow scoring streak with Kenny forced off in the ninth minute - Donal Keogan was introduced in his place.
Kenny's departure seemed to spur on his side as Meath began to create a series of decent scoring chances.
Reilly sent an effort off the post for the Royals before Joe Sheridan sliced through for the first clear-cut goal chance of the opening half. However, the big forward could not deliver and a rebound came off the opposite upright.
Brian Farrell, in his 33rd Championship appearance for Meath, managed to open their scoring account after 15 minutes.
Sheridan quickly added a point to make it 0-05 to 0-02 in the 16th minute, only for Wicklow to quickly respond with Hannon and Seanie Furlong both registering points.
But Meath were now battle-hardened and gained control in the midfield sector as they strung together five of the last six points before the break.
Farrell slotted over back-to-back points and debutants Mark Collins and Alan Forde, along with Reilly, also chipped in with scores. The spurt helped cut the gap to the minimum at the interval - 0-08 to 0-07.
Both sides played some entertaining football in the opening 35 minutes, and were reasonably clinical in front of the posts with Meath kicking four first half wides, while Wicklow sent two scoring opportunities wide of the target.
The sides emerged after a prolonged 19-minute break and it was McEnaney's charges who resumed in better fettle.
Reilly claiming his second point before play was held up for about six minutes after the influential Glynn sustained a knock to his right leg.
Wicklow's talisman had to be stretchered off after an accidental collision with Ward, with the latter grabbing a point to edge Meath in front for the first time in the 42nd minute.
It was the lead they would not relinquish and with Reilly in superb form they pushed into a 0-11 to 0-08 advantage with 25 minutes left on the clock.
Wicklow boss Harry Murphy brought Niall Gaffney on for Alan Byrne in the half-back line. Up front, changes were also made as the final quarter approached with John McGrath, scorer of three first-half points, making way and Avondale's Conor McGraynor introduced.
Hannon picked off his third point to cut the gap to two in the 55th minute, but Wicklow could only add one further point as their challenge wilted.
Although substitute McGraynor did his best to inspire the underdogs, Meath put in a strong defensive showing late on to sew up the result.
McGraynor was denied a goal following a fine save by Meath goalkeeper David Gallagher in the 62nd minute, while he was also forced wide late on.
Wicklow were reduced to 14 men with five minutes to go when midfielder Stafford was shown his second yellow card for a foul on Alan Forde.
Hannon made it a three-point game in the 73rd minute, but scores from Sheridan and substitute Jamie Queeney capped off an encouraging Meath performance deep into injury-time.
Scorers - Meath: G Reilly 0-05, B Farrell 0-04, J Sheridan, J Queeney 0-02 each, M Collins, A Forde, C Ward 0-01 each
Wicklow: T Hannon 0-05, S McGrath 0-03, J Stafford, S Furlong, R Finn 0-01 each
Meath: D Gallagher; M Burke, K Reilly, S McAnarney; D Tobin, B Menton, S Kenny; C Gillespie, B Meade; A Forde, M Collins, G Reilly; B Farrell, J Sheridan, C Ward.
Subs used: D Keogan for Kenny (9 mins), J Queeney for Collins (55), P Burke for G Reilly (64), B Sheridan for Ward (70), D Carroll for Forde (70+3).
Wicklow: J Flynn; C Hyland, A McLoughlin, A Byrne; D Healy, S Byrne, S Kelly; J Stafford, R Finn; D Hayden, D O'Sullivan, L Glynn; T Hannon, S Furlong, J McGrath.
Subs used: P Burke for O'Sullivan (half-time), P Earls for Glynn (41 mins), N Gaffney for A Byrne (47), C McGraynor for McGrath (51).
Referee: Padraig Hughes (Armagh)
